Solve 9%-9x^2*2/4^2-5x

$$9 \% -9 { x }^{ 2 } \times \frac { 2 } { { 4 }^{ 2 } -5x }$$

Evaluate

$$\frac{9\left(16-5x-200x^{2}\right)}{100\left(16-5x\right)}$$

Short Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{9}{100}-9x^{2}\times \frac{2}{16-5x}$$

Express 9\times \frac{2}{16-5x} as a single fraction.

$$\frac{9}{100}-\frac{9\times 2}{16-5x}x^{2}$$

Multiply 9 and 2 to get 18.

$$\frac{9}{100}-\frac{18}{16-5x}x^{2}$$

Express \frac{18}{16-5x}x^{2} as a single fraction.

$$\frac{9}{100}-\frac{18x^{2}}{16-5x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 100 and 16-5x is 100\left(-5x+16\right). Multiply \frac{9}{100} times \frac{-5x+16}{-5x+16}. Multiply \frac{18x^{2}}{16-5x} times \frac{100}{100}.

$$\frac{9\left(-5x+16\right)}{100\left(-5x+16\right)}-\frac{100\times 18x^{2}}{100\left(-5x+16\right)}$$

Since \frac{9\left(-5x+16\right)}{100\left(-5x+16\right)} and \frac{100\times 18x^{2}}{100\left(-5x+16\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\left(-5x+16\right)-100\times 18x^{2}}{100\left(-5x+16\right)}$$

Do the multiplications in 9\left(-5x+16\right)-100\times 18x^{2}.

$$\frac{-45x+144-1800x^{2}}{100\left(-5x+16\right)}$$

Factor the expressions that are not already factored in \frac{-45x+144-1800x^{2}}{100\left(-5x+16\right)}.

$$\frac{-9\times 200\left(x-\left(-\frac{3}{80}\sqrt{57}-\frac{1}{80}\right)\right)\left(x-\left(\frac{3}{80}\sqrt{57}-\frac{1}{80}\right)\right)}{100\left(-5x+16\right)}$$

Cancel out 100 in both numerator and denominator.

$$\frac{-2\times 9\left(x-\left(-\frac{3}{80}\sqrt{57}-\frac{1}{80}\right)\right)\left(x-\left(\frac{3}{80}\sqrt{57}-\frac{1}{80}\right)\right)}{-5x+16}$$

Multiply -2 and 9 to get -18.

$$\frac{-18\left(x-\left(-\frac{3}{80}\sqrt{57}-\frac{1}{80}\right)\right)\left(x-\left(\frac{3}{80}\sqrt{57}-\frac{1}{80}\right)\right)}{-5x+16}$$

To find the opposite of -\frac{3}{80}\sqrt{57}-\frac{1}{80}, find the opposite of each term.

$$\frac{-18\left(x+\frac{3}{80}\sqrt{57}+\frac{1}{80}\right)\left(x-\left(\frac{3}{80}\sqrt{57}-\frac{1}{80}\right)\right)}{-5x+16}$$

To find the opposite of \frac{3}{80}\sqrt{57}-\frac{1}{80}, find the opposite of each term.

$$\frac{-18\left(x+\frac{3}{80}\sqrt{57}+\frac{1}{80}\right)\left(x-\frac{3}{80}\sqrt{57}+\frac{1}{80}\right)}{-5x+16}$$

Use the distributive property to multiply -18 by x+\frac{3}{80}\sqrt{57}+\frac{1}{80}.

$$\frac{\left(-18x-\frac{27}{40}\sqrt{57}-\frac{9}{40}\right)\left(x-\frac{3}{80}\sqrt{57}+\frac{1}{80}\right)}{-5x+16}$$

Use the distributive property to multiply -18x-\frac{27}{40}\sqrt{57}-\frac{9}{40} by x-\frac{3}{80}\sqrt{57}+\frac{1}{80} and combine like terms.

$$\frac{-18x^{2}-\frac{9}{20}x+\frac{81}{3200}\left(\sqrt{57}\right)^{2}-\frac{9}{3200}}{-5x+16}$$

The square of \sqrt{57} is 57.

$$\frac{-18x^{2}-\frac{9}{20}x+\frac{81}{3200}\times 57-\frac{9}{3200}}{-5x+16}$$

Multiply \frac{81}{3200} and 57 to get \frac{4617}{3200}.

$$\frac{-18x^{2}-\frac{9}{20}x+\frac{4617}{3200}-\frac{9}{3200}}{-5x+16}$$

Subtract \frac{9}{3200} from \frac{4617}{3200} to get \frac{36}{25}.

$$\frac{-18x^{2}-\frac{9}{20}x+\frac{36}{25}}{-5x+16}$$

Factor

$$-\frac{18\left(x-\frac{-3\sqrt{57}-1}{80}\right)\left(x-\frac{3\sqrt{57}-1}{80}\right)}{16-5x}$$