Solve v^2=12v

$$v ^ { 2 } = 12 v$$

Solve for v

$$v=12$$

$$v=0$$

Steps Using Factoring

Subtract 12v from both sides.

$$v^{2}-12v=0$$

Factor out v.

$$v\left(v-12\right)=0$$

To find equation solutions, solve v=0 and v-12=0.

$$v=0 v=12$$

Steps Using the Quadratic Formula

Subtract 12v from both sides.

$$v^{2}-12v=0$$

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}.

$$v=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2}$$

Take the square root of \left(-12\right)^{2}.

$$v=\frac{-\left(-12\right)±12}{2}$$

The opposite of -12 is 12.

$$v=\frac{12±12}{2}$$

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

$$v=\frac{24}{2}$$

Divide 24 by 2.

$$v=12$$

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

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

Divide 0 by 2.

$$v=0$$

The equation is now solved.

$$v=12 v=0$$

Steps for Completing the Square

Subtract 12v from both sides.

$$v^{2}-12v=0$$

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.

$$v^{2}-12v+\left(-6\right)^{2}=\left(-6\right)^{2}$$

Square -6.

$$v^{2}-12v+36=36$$

Factor v^{2}-12v+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}.

$$\left(v-6\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(v-6\right)^{2}}=\sqrt{36}$$

Simplify.

$$v-6=6 v-6=-6$$

Add 6 to both sides of the equation.

$$v=12 v=0$$