Solve -x^2/25+4

$$\frac { - x ^ { 2 } } { 25 } + 4$$

Evaluate

$$-\frac{x^{2}}{25}+4$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{25}{25}.

$$\frac{-x^{2}}{25}+\frac{4\times 25}{25}$$

Since \frac{-x^{2}}{25} and \frac{4\times 25}{25} have the same denominator, add them by adding their numerators.

$$\frac{-x^{2}+4\times 25}{25}$$

Do the multiplications in -x^{2}+4\times 25.

$$\frac{-x^{2}+100}{25}$$

Factor

$$\frac{\left(-x-10\right)\left(x-10\right)}{25}$$

Solution Steps

Factor out \frac{1}{25}.

$$\frac{-x^{2}+100}{25}$$

Consider -x^{2}+100. Rewrite -x^{2}+100 as 10^{2}-x^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10-x\right)\left(10+x\right)$$

Reorder the terms.

$$\left(-x+10\right)\left(x+10\right)$$

Rewrite the complete factored expression.

$$\frac{\left(-x+10\right)\left(x+10\right)}{25}$$