Solve y=left(x+5right)^2+45

$$y= { \left(x+5 \right) }^{ 2 } +45$$

Solve for y

$$y=\left(x+5\right)^{2}+45$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$y=x^{2}+10x+25+45$$

Add 25 and 45 to get 70.

$$y=x^{2}+10x+70$$

Solve for x (complex solution)

$$x=-\left(\sqrt{y-45}+5\right)$$

$$x=\sqrt{y-45}-5$$

Solve for x

$$x=-\left(\sqrt{y-45}+5\right)$$

$$x=\sqrt{y-45}-5\text{, }y\geq 45$$