Solve Using the Quadratic Formula 5r^2=80

$5 r^{2} = 80$

Step 1

Subtract $80$ from both sides of the equation.

$5 r^{2} - 80 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 5$ , $b = 0$ , and $c = - 80$ into the quadratic formula and solve for $r$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (5 \cdot - 80)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$r = \frac{0 \pm \sqrt{0 - 4 \cdot 5 \cdot - 80}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 80$ .

Multiply $- 4$ by $5$ .

$r = \frac{0 \pm \sqrt{0 - 20 \cdot - 80}}{2 \cdot 5}$

Multiply $- 20$ by $- 80$ .

$r = \frac{0 \pm \sqrt{0 + 1600}}{2 \cdot 5}$

Add $0$ and $1600$ .

$r = \frac{0 \pm \sqrt{1600}}{2 \cdot 5}$

Rewrite $1600$ as $40^{2}$ .

$r = \frac{0 \pm \sqrt{40^{2}}}{2 \cdot 5}$

Pull terms out from under the radical, assuming positive real numbers.

$r = \frac{0 \pm 40}{2 \cdot 5}$

Multiply $2$ by $5$ .

$r = \frac{0 \pm 40}{10}$

Simplify $\frac{0 \pm 40}{10}$ .

$r = \pm 4$

Step 5

The final answer is the combination of both solutions.

$r = 4, - 4$