Solve x=sqrt{2y}-7

$$x= \sqrt{ 2y } -7$$

Solve for y

$$y=\frac{\left(x+7\right)^{2}}{2}$$

$$x\geq -7$$

Steps for Solving Radical Equations

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

$$\sqrt{2y}-7=x$$

Add 7 to both sides.

$$\sqrt{2y}=x+7$$

Square both sides of the equation.

$$2y=\left(x+7\right)^{2}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{\left(x+7\right)^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{\left(x+7\right)^{2}}{2}$$

Solve for y (complex solution)

$$y=\frac{\left(x+7\right)^{2}}{2}$$

$$arg(x+7)<\pi \text{ or }x=-7$$

Solve for x

$$x=\sqrt{2y}-7$$

$$y\geq 0$$