Solve Using the Quadratic Formula r^2-r=0

$r^{2} - r = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 1$ , $b = - 1$ , and $c = 0$ into the quadratic formula and solve for $r$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$r = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 0$ .

Multiply $- 4$ by $1$ .

$r = \frac{1 \pm \sqrt{1 - 4 \cdot 0}}{2 \cdot 1}$

Multiply $- 4$ by $0$ .

$r = \frac{1 \pm \sqrt{1 + 0}}{2 \cdot 1}$

Add $1$ and $0$ .

$r = \frac{1 \pm \sqrt{1}}{2 \cdot 1}$

Any root of $1$ is $1$ .

$r = \frac{1 \pm 1}{2 \cdot 1}$

Multiply $2$ by $1$ .

$r = \frac{1 \pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$r = 1, 0$