Solve x^2=-8x^

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

Solve for x

$$x=-8$$

$$x=0$$

Steps Using Factoring

Calculate x to the power of 1 and get x.

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

Add 8x to both sides.

$$x^{2}+8x=0$$

Factor out x.

$$x\left(x+8\right)=0$$

To find equation solutions, solve x=0 and x+8=0.

$$x=0 x=-8$$

Steps Using the Quadratic Formula

Calculate x to the power of 1 and get x.

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

Add 8x to both sides.

$$x^{2}+8x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}}}{2}$$

Take the square root of 8^{2}.

$$x=\frac{-8±8}{2}$$

Now solve the equation x=\frac{-8±8}{2} when ± is plus. Add -8 to 8.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-8±8}{2} when ± is minus. Subtract 8 from -8.

$$x=-\frac{16}{2}$$

Divide -16 by 2.

$$x=-8$$

The equation is now solved.

$$x=0 x=-8$$

Steps for Completing the Square

Calculate x to the power of 1 and get x.

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

Add 8x to both sides.

$$x^{2}+8x=0$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square 4.

$$x^{2}+8x+16=16$$

Factor x^{2}+8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{16}$$

Simplify.

$$x+4=4 x+4=-4$$

Subtract 4 from both sides of the equation.

$$x=0 x=-8$$