Solve x^2=-2(y-4.5)

$${ x }^{ 2 } =-2(y-4.5)$$

Solve for y

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

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by y-4.5.

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

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

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

Subtract 9 from both sides.

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

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

Divide x^{2}-9 by -2.

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

Solve for x (complex solution)

$$x=-\sqrt{9-2y}$$

$$x=\sqrt{9-2y}$$

Solve for x

$$x=\sqrt{9-2y}$$

$$x=-\sqrt{9-2y}\text{, }y\leq \frac{9}{2}$$