Solve y=1/5left(x+5right)^2-1

$$y= \frac{ 1 }{ 5 } { \left(x+5 \right) }^{ 2 } -1$$

Solve for y

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

Solution Steps

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

$$y=\frac{1}{5}\left(x^{2}+10x+25\right)-1$$

Use the distributive property to multiply \frac{1}{5} by x^{2}+10x+25.

$$y=\frac{1}{5}x^{2}+2x+5-1$$

Subtract 1 from 5 to get 4.

$$y=\frac{1}{5}x^{2}+2x+4$$

Solve for x (complex solution)

$$x=-\sqrt{5\left(y+1\right)}-5$$

$$x=\sqrt{5\left(y+1\right)}-5$$

Solve for x

$$x=-\sqrt{5\left(y+1\right)}-5$$

$$x=\sqrt{5\left(y+1\right)}-5\text{, }y\geq -1$$