Solve 3^2+y^2=2x-3^2

$$3 ^ { 2 } + y ^ { 2 } = 2 x - 3 ^ { 2 }$$

Solve for x

$$x=\frac{y^{2}+18}{2}$$

Steps for Solving Linear Equation

Calculate 3 to the power of 2 and get 9.

$$9+y^{2}=2x-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9+y^{2}=2x-9$$

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

$$2x-9=9+y^{2}$$

Add 9 to both sides.

$$2x=9+y^{2}+9$$

Add 9 and 9 to get 18.

$$2x=18+y^{2}$$

The equation is in standard form.

$$2x=y^{2}+18$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y^{2}+18}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y^{2}+18}{2}$$

Divide 18+y^{2} by 2.

$$x=\frac{y^{2}}{2}+9$$

Solve for y (complex solution)

$$y=-\sqrt{2\left(x-9\right)}$$

$$y=\sqrt{2\left(x-9\right)}$$

Solve for y

$$y=\sqrt{2\left(x-9\right)}$$

$$y=-\sqrt{2\left(x-9\right)}\text{, }x\geq 9$$