Solve x^2+bx+b^2/4=

$$x ^ { 2 } + b x + \frac { b ^ { 2 } } { 4 } =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+bx times \frac{4}{4}.

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

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

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

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

$$\frac{4x^{2}+4bx+b^{2}}{4}$$

Factor

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

Solution Steps

Factor out \frac{1}{4}.

$$\frac{4x^{2}+4bx+b^{2}}{4}$$

Consider 4x^{2}+4bx+b^{2}. Use the perfect square formula, p^{2}+2pq+q^{2}=\left(p+q\right)^{2}, where p=2x and q=b.

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

Rewrite the complete factored expression.

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