Solve =-95(4x/5-3)^2+2

$$= - 95 ( \frac { 4 x } { 5 } - 3 ) ^ { 2 } + 2$$

Evaluate

$$-\frac{19\left(4x-15\right)^{2}}{5}+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{5}{5}.

$$-95\left(\frac{4x}{5}-\frac{3\times 5}{5}\right)^{2}+2$$

Since \frac{4x}{5} and \frac{3\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$-95\times \left(\frac{4x-3\times 5}{5}\right)^{2}+2$$

Do the multiplications in 4x-3\times 5.

$$-95\times \left(\frac{4x-15}{5}\right)^{2}+2$$

To raise \frac{4x-15}{5} to a power, raise both numerator and denominator to the power and then divide.

$$-95\times \frac{\left(4x-15\right)^{2}}{5^{2}}+2$$

Express -95\times \frac{\left(4x-15\right)^{2}}{5^{2}} as a single fraction.

$$\frac{-95\left(4x-15\right)^{2}}{5^{2}}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5^{2}}{5^{2}}.

$$\frac{-95\left(4x-15\right)^{2}}{5^{2}}+\frac{2\times 5^{2}}{5^{2}}$$

Since \frac{-95\left(4x-15\right)^{2}}{5^{2}} and \frac{2\times 5^{2}}{5^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-95\left(4x-15\right)^{2}+2\times 5^{2}}{5^{2}}$$

Do the multiplications in -95\left(4x-15\right)^{2}+2\times 5^{2}.

$$\frac{-1520x^{2}+11400x-21375+50}{5^{2}}$$

Combine like terms in -1520x^{2}+11400x-21375+50.

$$\frac{-1520x^{2}+11400x-21325}{5^{2}}$$

Factor the expressions that are not already factored in \frac{-1520x^{2}+11400x-21325}{5^{2}}.

$$\frac{-5\times 304\left(x-\left(-\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)}{5^{2}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-304\left(x-\left(-\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)}{5}$$

To find the opposite of -\frac{1}{76}\sqrt{190}+\frac{15}{4}, find the opposite of each term.

$$\frac{-304\left(x+\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)\left(x-\left(\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)}{5}$$

To find the opposite of \frac{1}{76}\sqrt{190}+\frac{15}{4}, find the opposite of each term.

$$\frac{-304\left(x+\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)\left(x-\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)}{5}$$

Use the distributive property to multiply -304 by x+\frac{1}{76}\sqrt{190}-\frac{15}{4}.

$$\frac{\left(-304x-4\sqrt{190}+1140\right)\left(x-\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)}{5}$$

Use the distributive property to multiply -304x-4\sqrt{190}+1140 by x-\frac{1}{76}\sqrt{190}-\frac{15}{4} and combine like terms.

$$\frac{-304x^{2}+2280x+\frac{1}{19}\left(\sqrt{190}\right)^{2}-4275}{5}$$

The square of \sqrt{190} is 190.

$$\frac{-304x^{2}+2280x+\frac{1}{19}\times 190-4275}{5}$$

Multiply \frac{1}{19} and 190 to get 10.

$$\frac{-304x^{2}+2280x+10-4275}{5}$$

Subtract 4275 from 10 to get -4265.

$$\frac{-304x^{2}+2280x-4265}{5}$$

Expand

$$-\frac{304x^{2}}{5}+456x-853$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{5}{5}.

$$-95\left(\frac{4x}{5}-\frac{3\times 5}{5}\right)^{2}+2$$

Since \frac{4x}{5} and \frac{3\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$-95\times \left(\frac{4x-3\times 5}{5}\right)^{2}+2$$

Do the multiplications in 4x-3\times 5.

$$-95\times \left(\frac{4x-15}{5}\right)^{2}+2$$

To raise \frac{4x-15}{5} to a power, raise both numerator and denominator to the power and then divide.

$$-95\times \frac{\left(4x-15\right)^{2}}{5^{2}}+2$$

Express -95\times \frac{\left(4x-15\right)^{2}}{5^{2}} as a single fraction.

$$\frac{-95\left(4x-15\right)^{2}}{5^{2}}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5^{2}}{5^{2}}.

$$\frac{-95\left(4x-15\right)^{2}}{5^{2}}+\frac{2\times 5^{2}}{5^{2}}$$

Since \frac{-95\left(4x-15\right)^{2}}{5^{2}} and \frac{2\times 5^{2}}{5^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-95\left(4x-15\right)^{2}+2\times 5^{2}}{5^{2}}$$

Do the multiplications in -95\left(4x-15\right)^{2}+2\times 5^{2}.

$$\frac{-1520x^{2}+11400x-21375+50}{5^{2}}$$

Combine like terms in -1520x^{2}+11400x-21375+50.

$$\frac{-1520x^{2}+11400x-21325}{5^{2}}$$

Factor the expressions that are not already factored in \frac{-1520x^{2}+11400x-21325}{5^{2}}.

$$\frac{-5\times 304\left(x-\left(-\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)}{5^{2}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-304\left(x-\left(-\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)}{5}$$

To find the opposite of -\frac{1}{76}\sqrt{190}+\frac{15}{4}, find the opposite of each term.

$$\frac{-304\left(x+\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)\left(x-\left(\frac{1}{76}\sqrt{190}+\frac{15}{4}\right)\right)}{5}$$

To find the opposite of \frac{1}{76}\sqrt{190}+\frac{15}{4}, find the opposite of each term.

$$\frac{-304\left(x+\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)\left(x-\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)}{5}$$

Use the distributive property to multiply -304 by x+\frac{1}{76}\sqrt{190}-\frac{15}{4}.

$$\frac{\left(-304x-4\sqrt{190}+1140\right)\left(x-\frac{1}{76}\sqrt{190}-\frac{15}{4}\right)}{5}$$

Use the distributive property to multiply -304x-4\sqrt{190}+1140 by x-\frac{1}{76}\sqrt{190}-\frac{15}{4} and combine like terms.

$$\frac{-304x^{2}+2280x+\frac{1}{19}\left(\sqrt{190}\right)^{2}-4275}{5}$$

The square of \sqrt{190} is 190.

$$\frac{-304x^{2}+2280x+\frac{1}{19}\times 190-4275}{5}$$

Multiply \frac{1}{19} and 190 to get 10.

$$\frac{-304x^{2}+2280x+10-4275}{5}$$

Subtract 4275 from 10 to get -4265.

$$\frac{-304x^{2}+2280x-4265}{5}$$