Solve x^2=-{left(sqrt{4y-8}right)}^2

$${ x }^{ 2 } = - { \left( \sqrt{ 4y-8 } \right) }^{ 2 }$$

Solve for y (complex solution)

$$y=-\frac{x^{2}}{4}+2$$

Steps for Solving Linear Equation

Calculate \sqrt{4y-8} to the power of 2 and get 4y-8.

$$x^{2}=-\left(4y-8\right)$$

To find the opposite of 4y-8, find the opposite of each term.

$$x^{2}=-4y+8$$

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

$$-4y+8=x^{2}$$

Subtract 8 from both sides.

$$-4y=x^{2}-8$$

Divide both sides by -4.

$$\frac{-4y}{-4}=\frac{x^{2}-8}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$y=\frac{x^{2}-8}{-4}$$

Divide x^{2}-8 by -4.

$$y=-\frac{x^{2}}{4}+2$$

Solve for y

$$y=2$$

$$x=0$$

Steps for Solving Linear Equation

Calculate \sqrt{4y-8} to the power of 2 and get 4y-8.

$$x^{2}=-\left(4y-8\right)$$

To find the opposite of 4y-8, find the opposite of each term.

$$x^{2}=-4y+8$$

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

$$-4y+8=x^{2}$$

Subtract 8 from both sides.

$$-4y=x^{2}-8$$

Divide both sides by -4.

$$\frac{-4y}{-4}=\frac{x^{2}-8}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$y=\frac{x^{2}-8}{-4}$$

Divide x^{2}-8 by -4.

$$y=-\frac{x^{2}}{4}+2$$

Solve for x (complex solution)

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

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

Solve for x

$$x=0$$

$$y=2$$