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

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

Solve for y

$$y=\frac{\left(x+2\right)^{2}+24}{8}$$

Steps for Solving Linear Equation

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

$$x^{2}+4x+4=8\left(y-3\right)$$

Use the distributive property to multiply 8 by y-3.

$$x^{2}+4x+4=8y-24$$

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

$$8y-24=x^{2}+4x+4$$

Add 24 to both sides.

$$8y=x^{2}+4x+4+24$$

Add 4 and 24 to get 28.

$$8y=x^{2}+4x+28$$

Divide both sides by 8.

$$\frac{8y}{8}=\frac{x^{2}+4x+28}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$y=\frac{x^{2}+4x+28}{8}$$

Divide x^{2}+4x+28 by 8.

$$y=\frac{x^{2}}{8}+\frac{x}{2}+\frac{7}{2}$$

Solve for x (complex solution)

$$x=-2\sqrt{2y-6}-2$$

$$x=2\sqrt{2y-6}-2$$

Solve for x

$$x=-2\sqrt{2y-6}-2$$

$$x=2\sqrt{2y-6}-2\text{, }y\geq 3$$