Solve w^2=-12w

$$w ^ { 2 } = - 12 w$$

Solve for w

$$w=-12$$

$$w=0$$

Steps Using Factoring

Add 12w to both sides.

$$w^{2}+12w=0$$

Factor out w.

$$w\left(w+12\right)=0$$

To find equation solutions, solve w=0 and w+12=0.

$$w=0 w=-12$$

Steps Using the Quadratic Formula

Add 12w to both sides.

$$w^{2}+12w=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 12 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-12±\sqrt{12^{2}}}{2}$$

Take the square root of 12^{2}.

$$w=\frac{-12±12}{2}$$

Now solve the equation w=\frac{-12±12}{2} when ± is plus. Add -12 to 12.

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

Divide 0 by 2.

$$w=0$$

Now solve the equation w=\frac{-12±12}{2} when ± is minus. Subtract 12 from -12.

$$w=-\frac{24}{2}$$

Divide -24 by 2.

$$w=-12$$

The equation is now solved.

$$w=0 w=-12$$

Steps for Completing the Square

Add 12w to both sides.

$$w^{2}+12w=0$$

Divide 12, the coefficient of the x term, by 2 to get 6. Then add the square of 6 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}+12w+6^{2}=6^{2}$$

Square 6.

$$w^{2}+12w+36=36$$

Factor w^{2}+12w+36. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(w+6\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w+6\right)^{2}}=\sqrt{36}$$

Simplify.

$$w+6=6 w+6=-6$$

Subtract 6 from both sides of the equation.

$$w=0 w=-12$$