Solve (y-5)^2=8(x+3)

$$( y - 5 ) ^ { 2 } = 8 ( x + 3 )$$

Solve for x

$$x=\frac{\left(y-5\right)^{2}-24}{8}$$

Steps for Solving Linear Equation

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

$$y^{2}-10y+25=8\left(x+3\right)$$

Use the distributive property to multiply 8 by x+3.

$$y^{2}-10y+25=8x+24$$

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

$$8x+24=y^{2}-10y+25$$

Subtract 24 from both sides.

$$8x=y^{2}-10y+25-24$$

Subtract 24 from 25 to get 1.

$$8x=y^{2}-10y+1$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{y^{2}-10y+1}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{y^{2}-10y+1}{8}$$

Divide y^{2}-10y+1 by 8.

$$x=\frac{y^{2}}{8}-\frac{5y}{4}+\frac{1}{8}$$

Solve for y (complex solution)

$$y=-2\sqrt{2\left(x+3\right)}+5$$

$$y=2\sqrt{2\left(x+3\right)}+5$$

Solve for y

$$y=-2\sqrt{2\left(x+3\right)}+5$$

$$y=2\sqrt{2\left(x+3\right)}+5\text{, }x\geq -3$$