Solve p^2=2p

$$p ^ { 2 } = 2 p$$

Solve for p

$$p=2$$

$$p=0$$

Steps Using Factoring

Subtract 2p from both sides.

$$p^{2}-2p=0$$

Factor out p.

$$p\left(p-2\right)=0$$

To find equation solutions, solve p=0 and p-2=0.

$$p=0 p=2$$

Steps Using the Quadratic Formula

Subtract 2p from both sides.

$$p^{2}-2p=0$$

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

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

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

$$p=\frac{-\left(-2\right)±2}{2}$$

The opposite of -2 is 2.

$$p=\frac{2±2}{2}$$

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

$$p=\frac{4}{2}$$

Divide 4 by 2.

$$p=2$$

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

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

Divide 0 by 2.

$$p=0$$

The equation is now solved.

$$p=2 p=0$$

Steps for Completing the Square

Subtract 2p from both sides.

$$p^{2}-2p=0$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$p^{2}-2p+1=1$$

Factor p^{2}-2p+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(p-1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(p-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$p-1=1 p-1=-1$$

Add 1 to both sides of the equation.

$$p=2 p=0$$