Solve y-x^2-2x-15/2=2

$$y- \frac{ { x }^{ 2 } -2x-15 }{ 2 } = 2$$

Solve for y

$$y=\frac{x^{2}-2x-11}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2y-\left(x^{2}-2x-15\right)=4$$

To find the opposite of x^{2}-2x-15, find the opposite of each term.

$$2y-x^{2}+2x+15=4$$

Add x^{2} to both sides.

$$2y+2x+15=4+x^{2}$$

Subtract 2x from both sides.

$$2y+15=4+x^{2}-2x$$

Subtract 15 from both sides.

$$2y=4+x^{2}-2x-15$$

Subtract 15 from 4 to get -11.

$$2y=-11+x^{2}-2x$$

The equation is in standard form.

$$2y=x^{2}-2x-11$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{x^{2}-2x-11}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{x^{2}-2x-11}{2}$$

Divide -11+x^{2}-2x by 2.

$$y=\frac{x^{2}}{2}-x-\frac{11}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{2\left(y+6\right)}+1$$

$$x=\sqrt{2\left(y+6\right)}+1$$

Solve for x

$$x=-\sqrt{2\left(y+6\right)}+1$$

$$x=\sqrt{2\left(y+6\right)}+1\text{, }y\geq -6$$