Solve 2x^2+2y-12x+8=24

$$2 { x }^{ 2 } +2y-12x+8=24$$

Solve for y

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

Steps for Solving Linear Equation

Subtract 2x^{2} from both sides.

$$2y-12x+8=24-2x^{2}$$

Add 12x to both sides.

$$2y+8=24-2x^{2}+12x$$

Subtract 8 from both sides.

$$2y=24-2x^{2}+12x-8$$

Subtract 8 from 24 to get 16.

$$2y=16-2x^{2}+12x$$

The equation is in standard form.

$$2y=16+12x-2x^{2}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{16+12x-2x^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{16+12x-2x^{2}}{2}$$

Divide 16-2x^{2}+12x by 2.

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

Solve for x (complex solution)

$$x=\sqrt{17-y}+3$$

$$x=-\sqrt{17-y}+3$$

Solve for x

$$x=\sqrt{17-y}+3$$

$$x=-\sqrt{17-y}+3\text{, }y\leq 17$$