Solve sqrt{25/4}-3+left(x+2right)^2

$$\sqrt{ \frac{ 25 }{ 4 } } -3+ { \left(x+2 \right) }^{ 2 }$$

Evaluate

$$\left(x+2\right)^{2}-\frac{1}{2}$$

Solution Steps

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

Subtract 3 from \frac{5}{2} to get -\frac{1}{2}.

$$-\frac{1}{2}+\left(x+2\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$-\frac{1}{2}+x^{2}+4x+4$$

Add -\frac{1}{2} and 4 to get \frac{7}{2}.

$$\frac{7}{2}+x^{2}+4x$$

Factor

$$\left(x-\left(-\frac{\sqrt{2}}{2}-2\right)\right)\left(x-\left(\frac{\sqrt{2}}{2}-2\right)\right)$$