Solve -1593/28+2321/400x-2419/400(0.21-x)

$$- \frac { 1593 } { 28 } + \frac { 2321 } { 400 x } - \frac { 2419 } { 400 ( 0.21 - x ) }$$

Evaluate

$$\frac{3\left(5310000x^{2}-2221100x+113729\right)}{280000x\left(0.21-x\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 28 and 400x is 2800x. Multiply -\frac{1593}{28} times \frac{100x}{100x}. Multiply \frac{2321}{400x} times \frac{7}{7}.

$$-\frac{1593\times 100x}{2800x}+\frac{2321\times 7}{2800x}-\frac{2419}{400\left(0.21-x\right)}$$

Since -\frac{1593\times 100x}{2800x} and \frac{2321\times 7}{2800x} have the same denominator, add them by adding their numerators.

$$\frac{-1593\times 100x+2321\times 7}{2800x}-\frac{2419}{400\left(0.21-x\right)}$$

Do the multiplications in -1593\times 100x+2321\times 7.

$$\frac{-159300x+16247}{2800x}-\frac{2419}{400\left(0.21-x\right)}$$

Use the distributive property to multiply 400 by 0.21-x.

$$\frac{-159300x+16247}{2800x}-\frac{2419}{84-400x}$$

Factor 84-400x.

$$\frac{-159300x+16247}{2800x}-\frac{2419}{4\left(-100x+21\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2800x and 4\left(-100x+21\right) is 2800x\left(100x-21\right). Multiply \frac{-159300x+16247}{2800x} times \frac{100x-21}{100x-21}. Multiply \frac{2419}{4\left(-100x+21\right)} times \frac{-700x}{-700x}.

$$\frac{\left(-159300x+16247\right)\left(100x-21\right)}{2800x\left(100x-21\right)}-\frac{2419\left(-700\right)x}{2800x\left(100x-21\right)}$$

Since \frac{\left(-159300x+16247\right)\left(100x-21\right)}{2800x\left(100x-21\right)} and \frac{2419\left(-700\right)x}{2800x\left(100x-21\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(-159300x+16247\right)\left(100x-21\right)-2419\left(-700\right)x}{2800x\left(100x-21\right)}$$

Do the multiplications in \left(-159300x+16247\right)\left(100x-21\right)-2419\left(-700\right)x.

$$\frac{-15930000x^{2}+3345300x+1624700x-341187+1693300x}{2800x\left(100x-21\right)}$$

Combine like terms in -15930000x^{2}+3345300x+1624700x-341187+1693300x.

$$\frac{-15930000x^{2}+6663300x-341187}{2800x\left(100x-21\right)}$$

Factor the expressions that are not already factored in \frac{-15930000x^{2}+6663300x-341187}{2800x\left(100x-21\right)}.

$$\frac{-3\times 5310000\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{2800x\left(100x-21\right)}$$

Cancel out 400 in both numerator and denominator.

$$\frac{-3\times 13275\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{7x\left(100x-21\right)}$$

Expand 7x\left(100x-21\right).

$$\frac{-3\times 13275\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

Multiply -3 and 13275 to get -39825.

$$\frac{-39825\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

To find the opposite of -\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}, find the opposite of each term.

$$\frac{-39825\left(x-\left(-\frac{7}{4248}\sqrt{8221}\right)-\frac{22211}{106200}\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

The opposite of -\frac{7}{4248}\sqrt{8221} is \frac{7}{4248}\sqrt{8221}.

$$\frac{-39825\left(x+\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

To find the opposite of \frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}, find the opposite of each term.

$$\frac{-39825\left(x+\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Use the distributive property to multiply -39825 by x+\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}.

$$\frac{\left(-39825x-39825\times \frac{7}{4248}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\times \frac{7}{4248} as a single fraction.

$$\frac{\left(-39825x+\frac{-39825\times 7}{4248}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and 7 to get -278775.

$$\frac{\left(-39825x+\frac{-278775}{4248}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{-278775}{4248} to lowest terms by extracting and canceling out 531.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\left(-\frac{22211}{106200}\right) as a single fraction.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}+\frac{-39825\left(-22211\right)}{106200}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and -22211 to get 884553075.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}+\frac{884553075}{106200}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{884553075}{106200} to lowest terms by extracting and canceling out 13275.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}+\frac{66633}{8}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Apply the distributive property by multiplying each term of -39825x-\frac{525}{8}\sqrt{8221}+\frac{66633}{8} by each term of x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}.

$$\frac{-39825x^{2}-39825x\left(-\frac{7}{4248}\right)\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\sqrt{8221}\left(-\frac{7}{4248}\right)\sqrt{8221}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply \sqrt{8221} and \sqrt{8221} to get 8221.

$$\frac{-39825x^{2}-39825x\left(-\frac{7}{4248}\right)\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\left(-\frac{7}{4248}\right) as a single fraction.

$$\frac{-39825x^{2}+\frac{-39825\left(-7\right)}{4248}x\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and -7 to get 278775.

$$\frac{-39825x^{2}+\frac{278775}{4248}x\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{278775}{4248} to lowest terms by extracting and canceling out 531.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\left(-\frac{22211}{106200}\right) as a single fraction.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}+\frac{-39825\left(-22211\right)}{106200}x-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and -22211 to get 884553075.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}+\frac{884553075}{106200}x-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{884553075}{106200} to lowest terms by extracting and canceling out 13275.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}+\frac{66633}{8}x-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Combine \frac{525}{8}x\sqrt{8221} and -\frac{525}{8}\sqrt{8221}x to get 0.

$$\frac{-39825x^{2}+\frac{66633}{8}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -\frac{525}{8}\times 8221 as a single fraction.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{-525\times 8221}{8}\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -525 and 8221 to get -4316025.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{-4316025}{8}\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Fraction \frac{-4316025}{8} can be rewritten as -\frac{4316025}{8} by extracting the negative sign.

$$\frac{-39825x^{2}+\frac{66633}{8}x-\frac{4316025}{8}\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -\frac{4316025}{8} times -\frac{7}{4248} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{-4316025\left(-7\right)}{8\times 4248}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{-4316025\left(-7\right)}{8\times 4248}.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{30212175}{33984}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{30212175}{33984} to lowest terms by extracting and canceling out 3.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -\frac{525}{8} times -\frac{22211}{106200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}+\frac{-525\left(-22211\right)}{8\times 106200}\sqrt{8221}+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{-525\left(-22211\right)}{8\times 106200}.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}+\frac{11660775}{849600}\sqrt{8221}+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{11660775}{849600} to lowest terms by extracting and canceling out 75.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Combine \frac{66633}{8}x and \frac{66633}{8}x to get \frac{66633}{4}x.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply \frac{66633}{8} times -\frac{7}{4248} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{66633\left(-7\right)}{8\times 4248}\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{66633\left(-7\right)}{8\times 4248}.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{-466431}{33984}\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{-466431}{33984} to lowest terms by extracting and canceling out 3.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}-\frac{155477}{11328}\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Combine \frac{155477}{11328}\sqrt{8221} and -\frac{155477}{11328}\sqrt{8221} to get 0.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply \frac{66633}{8} times -\frac{22211}{106200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{66633\left(-22211\right)}{8\times 106200}}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{66633\left(-22211\right)}{8\times 106200}.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{-1479985563}{849600}}{700x^{2}-147x}$$

Reduce the fraction \frac{-1479985563}{849600} to lowest terms by extracting and canceling out 3.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}-\frac{493328521}{283200}}{700x^{2}-147x}$$

Least common multiple of 11328 and 283200 is 283200. Convert \frac{10070725}{11328} and \frac{493328521}{283200} to fractions with denominator 283200.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{251768125}{283200}-\frac{493328521}{283200}}{700x^{2}-147x}$$

Since \frac{251768125}{283200} and \frac{493328521}{283200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{251768125-493328521}{283200}}{700x^{2}-147x}$$

Subtract 493328521 from 251768125 to get -241560396.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{-241560396}{283200}}{700x^{2}-147x}$$

Reduce the fraction \frac{-241560396}{283200} to lowest terms by extracting and canceling out 708.

$$\frac{-39825x^{2}+\frac{66633}{4}x-\frac{341187}{400}}{700x^{2}-147x}$$

Expand

$$\frac{3\left(5310000x^{2}-2221100x+113729\right)}{280000x\left(0.21-x\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 28 and 400x is 2800x. Multiply -\frac{1593}{28} times \frac{100x}{100x}. Multiply \frac{2321}{400x} times \frac{7}{7}.

$$-\frac{1593\times 100x}{2800x}+\frac{2321\times 7}{2800x}-\frac{2419}{400\left(0.21-x\right)}$$

Since -\frac{1593\times 100x}{2800x} and \frac{2321\times 7}{2800x} have the same denominator, add them by adding their numerators.

$$\frac{-1593\times 100x+2321\times 7}{2800x}-\frac{2419}{400\left(0.21-x\right)}$$

Do the multiplications in -1593\times 100x+2321\times 7.

$$\frac{-159300x+16247}{2800x}-\frac{2419}{400\left(0.21-x\right)}$$

Use the distributive property to multiply 400 by 0.21-x.

$$\frac{-159300x+16247}{2800x}-\frac{2419}{84-400x}$$

Factor 84-400x.

$$\frac{-159300x+16247}{2800x}-\frac{2419}{4\left(-100x+21\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2800x and 4\left(-100x+21\right) is 2800x\left(100x-21\right). Multiply \frac{-159300x+16247}{2800x} times \frac{100x-21}{100x-21}. Multiply \frac{2419}{4\left(-100x+21\right)} times \frac{-700x}{-700x}.

$$\frac{\left(-159300x+16247\right)\left(100x-21\right)}{2800x\left(100x-21\right)}-\frac{2419\left(-700\right)x}{2800x\left(100x-21\right)}$$

Since \frac{\left(-159300x+16247\right)\left(100x-21\right)}{2800x\left(100x-21\right)} and \frac{2419\left(-700\right)x}{2800x\left(100x-21\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(-159300x+16247\right)\left(100x-21\right)-2419\left(-700\right)x}{2800x\left(100x-21\right)}$$

Do the multiplications in \left(-159300x+16247\right)\left(100x-21\right)-2419\left(-700\right)x.

$$\frac{-15930000x^{2}+3345300x+1624700x-341187+1693300x}{2800x\left(100x-21\right)}$$

Combine like terms in -15930000x^{2}+3345300x+1624700x-341187+1693300x.

$$\frac{-15930000x^{2}+6663300x-341187}{2800x\left(100x-21\right)}$$

Factor the expressions that are not already factored in \frac{-15930000x^{2}+6663300x-341187}{2800x\left(100x-21\right)}.

$$\frac{-3\times 5310000\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{2800x\left(100x-21\right)}$$

Cancel out 400 in both numerator and denominator.

$$\frac{-3\times 13275\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{7x\left(100x-21\right)}$$

Expand 7x\left(100x-21\right).

$$\frac{-3\times 13275\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

Multiply -3 and 13275 to get -39825.

$$\frac{-39825\left(x-\left(-\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

To find the opposite of -\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}, find the opposite of each term.

$$\frac{-39825\left(x-\left(-\frac{7}{4248}\sqrt{8221}\right)-\frac{22211}{106200}\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

The opposite of -\frac{7}{4248}\sqrt{8221} is \frac{7}{4248}\sqrt{8221}.

$$\frac{-39825\left(x+\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)\left(x-\left(\frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}\right)\right)}{700x^{2}-147x}$$

To find the opposite of \frac{7}{4248}\sqrt{8221}+\frac{22211}{106200}, find the opposite of each term.

$$\frac{-39825\left(x+\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Use the distributive property to multiply -39825 by x+\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}.

$$\frac{\left(-39825x-39825\times \frac{7}{4248}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\times \frac{7}{4248} as a single fraction.

$$\frac{\left(-39825x+\frac{-39825\times 7}{4248}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and 7 to get -278775.

$$\frac{\left(-39825x+\frac{-278775}{4248}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{-278775}{4248} to lowest terms by extracting and canceling out 531.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}-39825\left(-\frac{22211}{106200}\right)\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\left(-\frac{22211}{106200}\right) as a single fraction.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}+\frac{-39825\left(-22211\right)}{106200}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and -22211 to get 884553075.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}+\frac{884553075}{106200}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{884553075}{106200} to lowest terms by extracting and canceling out 13275.

$$\frac{\left(-39825x-\frac{525}{8}\sqrt{8221}+\frac{66633}{8}\right)\left(x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Apply the distributive property by multiplying each term of -39825x-\frac{525}{8}\sqrt{8221}+\frac{66633}{8} by each term of x-\frac{7}{4248}\sqrt{8221}-\frac{22211}{106200}.

$$\frac{-39825x^{2}-39825x\left(-\frac{7}{4248}\right)\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\sqrt{8221}\left(-\frac{7}{4248}\right)\sqrt{8221}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply \sqrt{8221} and \sqrt{8221} to get 8221.

$$\frac{-39825x^{2}-39825x\left(-\frac{7}{4248}\right)\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\left(-\frac{7}{4248}\right) as a single fraction.

$$\frac{-39825x^{2}+\frac{-39825\left(-7\right)}{4248}x\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and -7 to get 278775.

$$\frac{-39825x^{2}+\frac{278775}{4248}x\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{278775}{4248} to lowest terms by extracting and canceling out 531.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}-39825x\left(-\frac{22211}{106200}\right)-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -39825\left(-\frac{22211}{106200}\right) as a single fraction.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}+\frac{-39825\left(-22211\right)}{106200}x-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -39825 and -22211 to get 884553075.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}+\frac{884553075}{106200}x-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{884553075}{106200} to lowest terms by extracting and canceling out 13275.

$$\frac{-39825x^{2}+\frac{525}{8}x\sqrt{8221}+\frac{66633}{8}x-\frac{525}{8}\sqrt{8221}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Combine \frac{525}{8}x\sqrt{8221} and -\frac{525}{8}\sqrt{8221}x to get 0.

$$\frac{-39825x^{2}+\frac{66633}{8}x-\frac{525}{8}\times 8221\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Express -\frac{525}{8}\times 8221 as a single fraction.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{-525\times 8221}{8}\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -525 and 8221 to get -4316025.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{-4316025}{8}\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Fraction \frac{-4316025}{8} can be rewritten as -\frac{4316025}{8} by extracting the negative sign.

$$\frac{-39825x^{2}+\frac{66633}{8}x-\frac{4316025}{8}\left(-\frac{7}{4248}\right)-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -\frac{4316025}{8} times -\frac{7}{4248} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{-4316025\left(-7\right)}{8\times 4248}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{-4316025\left(-7\right)}{8\times 4248}.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{30212175}{33984}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{30212175}{33984} to lowest terms by extracting and canceling out 3.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}-\frac{525}{8}\sqrt{8221}\left(-\frac{22211}{106200}\right)+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply -\frac{525}{8} times -\frac{22211}{106200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}+\frac{-525\left(-22211\right)}{8\times 106200}\sqrt{8221}+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{-525\left(-22211\right)}{8\times 106200}.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}+\frac{11660775}{849600}\sqrt{8221}+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{11660775}{849600} to lowest terms by extracting and canceling out 75.

$$\frac{-39825x^{2}+\frac{66633}{8}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{66633}{8}x+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Combine \frac{66633}{8}x and \frac{66633}{8}x to get \frac{66633}{4}x.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{66633}{8}\left(-\frac{7}{4248}\right)\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply \frac{66633}{8} times -\frac{7}{4248} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{66633\left(-7\right)}{8\times 4248}\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{66633\left(-7\right)}{8\times 4248}.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}+\frac{-466431}{33984}\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Reduce the fraction \frac{-466431}{33984} to lowest terms by extracting and canceling out 3.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{155477}{11328}\sqrt{8221}-\frac{155477}{11328}\sqrt{8221}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Combine \frac{155477}{11328}\sqrt{8221} and -\frac{155477}{11328}\sqrt{8221} to get 0.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{66633}{8}\left(-\frac{22211}{106200}\right)}{700x^{2}-147x}$$

Multiply \frac{66633}{8} times -\frac{22211}{106200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{66633\left(-22211\right)}{8\times 106200}}{700x^{2}-147x}$$

Do the multiplications in the fraction \frac{66633\left(-22211\right)}{8\times 106200}.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}+\frac{-1479985563}{849600}}{700x^{2}-147x}$$

Reduce the fraction \frac{-1479985563}{849600} to lowest terms by extracting and canceling out 3.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{10070725}{11328}-\frac{493328521}{283200}}{700x^{2}-147x}$$

Least common multiple of 11328 and 283200 is 283200. Convert \frac{10070725}{11328} and \frac{493328521}{283200} to fractions with denominator 283200.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{251768125}{283200}-\frac{493328521}{283200}}{700x^{2}-147x}$$

Since \frac{251768125}{283200} and \frac{493328521}{283200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{251768125-493328521}{283200}}{700x^{2}-147x}$$

Subtract 493328521 from 251768125 to get -241560396.

$$\frac{-39825x^{2}+\frac{66633}{4}x+\frac{-241560396}{283200}}{700x^{2}-147x}$$

Reduce the fraction \frac{-241560396}{283200} to lowest terms by extracting and canceling out 708.

$$\frac{-39825x^{2}+\frac{66633}{4}x-\frac{341187}{400}}{700x^{2}-147x}$$