Solve y^2+x+15=3+2(x-1)

$$y ^ { 2 } + x + 15 = 3 + 2 ( x - 1 )$$

Solve for x

$$x=y^{2}+14$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-1.

$$y^{2}+x+15=3+2x-2$$

Subtract 2 from 3 to get 1.

$$y^{2}+x+15=1+2x$$

Subtract 2x from both sides.

$$y^{2}+x+15-2x=1$$

Combine x and -2x to get -x.

$$y^{2}-x+15=1$$

Subtract y^{2} from both sides.

$$-x+15=1-y^{2}$$

Subtract 15 from both sides.

$$-x=1-y^{2}-15$$

Subtract 15 from 1 to get -14.

$$-x=-14-y^{2}$$

The equation is in standard form.

$$-x=-y^{2}-14$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{-y^{2}-14}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{-y^{2}-14}{-1}$$

Divide -14-y^{2} by -1.

$$x=y^{2}+14$$

Solve for y (complex solution)

$$y=-\sqrt{x-14}$$

$$y=\sqrt{x-14}$$

Solve for y

$$y=\sqrt{x-14}$$

$$y=-\sqrt{x-14}\text{, }x\geq 14$$