Solve b^2=2b

$$b ^ { 2 } = 2 b$$

Solve for b

$$b=2$$

$$b=0$$

Steps Using Factoring

Subtract 2b from both sides.

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

Factor out b.

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

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

$$b=0 b=2$$

Steps Using the Quadratic Formula

Subtract 2b from both sides.

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

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}.

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

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

$$b=\frac{-\left(-2\right)±2}{2}$$

The opposite of -2 is 2.

$$b=\frac{2±2}{2}$$

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

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

Divide 4 by 2.

$$b=2$$

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

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

Divide 0 by 2.

$$b=0$$

The equation is now solved.

$$b=2 b=0$$

Steps for Completing the Square

Subtract 2b from both sides.

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

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.

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

Factor b^{2}-2b+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}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$b-1=1 b-1=-1$$

Add 1 to both sides of the equation.

$$b=2 b=0$$