Solve -8(y+2)=(x+1)^2

$$- 8 ( y + 2 ) = ( x + 1 ) ^ { 2 }$$

Solve for y

$$y=-\frac{\left(x+1\right)^{2}}{8}-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply -8 by y+2.

$$-8y-16=\left(x+1\right)^{2}$$

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

$$-8y-16=x^{2}+2x+1$$

Add 16 to both sides.

$$-8y=x^{2}+2x+1+16$$

Add 1 and 16 to get 17.

$$-8y=x^{2}+2x+17$$

Divide both sides by -8.

$$\frac{-8y}{-8}=\frac{x^{2}+2x+17}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$y=\frac{x^{2}+2x+17}{-8}$$

Divide x^{2}+2x+17 by -8.

$$y=-\frac{x^{2}}{8}-\frac{x}{4}-\frac{17}{8}$$

Solve for x (complex solution)

$$x=-2\sqrt{-2y-4}-1$$

$$x=2\sqrt{-2y-4}-1$$

Solve for x

$$x=-2\sqrt{-2y-4}-1$$

$$x=2\sqrt{-2y-4}-1\text{, }y\leq -2$$