Solve Using the Quadratic Formula x^2+7x-80=0

$x^{2} + 7 x - 80 = 0$

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 $a = 1$ , $b = 7$ , and $c = - 80$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot - 80)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot - 80}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 80$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 80}}{2 \cdot 1}$

Multiply $- 4$ by $- 80$ .

$x = \frac{- 7 \pm \sqrt{49 + 320}}{2 \cdot 1}$

Add $49$ and $320$ .

$x = \frac{- 7 \pm \sqrt{369}}{2 \cdot 1}$

Rewrite $369$ as $3^{2} \cdot 41$ .

Factor $9$ out of $369$ .

$x = \frac{- 7 \pm \sqrt{9 (41)}}{2 \cdot 1}$

Rewrite $9$ as $3^{2}$ .

$x = \frac{- 7 \pm \sqrt{3^{2} \cdot 41}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 7 \pm 3 \sqrt{41}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm 3 \sqrt{41}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 7 \pm 3 \sqrt{41}}{2}$

Decimal Form:

$x = 6.10468635 \dots, - 13.10468635 \dots$