Solve x^2+{left(1/2x+2right)}^2

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}x+2\right)^{2}.

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

Combine x^{2} and \frac{1}{4}x^{2} to get \frac{5}{4}x^{2}.

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

Expand

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}x+2\right)^{2}.

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

Combine x^{2} and \frac{1}{4}x^{2} to get \frac{5}{4}x^{2}.

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