Solve x^2/4+5x+25=

$$\frac { x ^ { 2 } } { 4 } + 5 x + 25 =$$

Evaluate

$$\frac{\left(x+10\right)^{2}}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x+25 times \frac{4}{4}.

$$\frac{x^{2}}{4}+\frac{4\left(5x+25\right)}{4}$$

Since \frac{x^{2}}{4} and \frac{4\left(5x+25\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+4\left(5x+25\right)}{4}$$

Do the multiplications in x^{2}+4\left(5x+25\right).

$$\frac{x^{2}+20x+100}{4}$$

Factor

$$\frac{\left(x+10\right)^{2}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x^{2}+20x+100}{4}$$

Consider x^{2}+20x+100. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x and b=10.

$$\left(x+10\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(x+10\right)^{2}}{4}$$