Solve (x-3)^2=8(y+2)

$$( x - 3 ) ^ { 2 } = 8 ( y + 2 )$$

Solve for y

$$y=\frac{\left(x-7\right)\left(x+1\right)}{8}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-6x+9=8\left(y+2\right)$$

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

$$x^{2}-6x+9=8y+16$$

Swap sides so that all variable terms are on the left hand side.

$$8y+16=x^{2}-6x+9$$

Subtract 16 from both sides.

$$8y=x^{2}-6x+9-16$$

Subtract 16 from 9 to get -7.

$$8y=x^{2}-6x-7$$

Divide both sides by 8.

$$\frac{8y}{8}=\frac{\left(x-7\right)\left(x+1\right)}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$y=\frac{\left(x-7\right)\left(x+1\right)}{8}$$

Solve for x (complex solution)

$$x=-2\sqrt{2\left(y+2\right)}+3$$

$$x=2\sqrt{2\left(y+2\right)}+3$$

Solve for x

$$x=-2\sqrt{2\left(y+2\right)}+3$$

$$x=2\sqrt{2\left(y+2\right)}+3\text{, }y\geq -2$$