Solve Using the Quadratic Formula x^2-19x+80=-8

$x^{2} - 19 x + 80 = - 8$

Step 1

Move all terms to the left side of the equation and simplify.

Add $8$ to both sides of the equation.

$x^{2} - 19 x + 80 + 8 = 0$

Add $80$ and $8$ .

$x^{2} - 19 x + 88 = 0$

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 $a = 1$ , $b = - 19$ , and $c = 88$ into the quadratic formula and solve for $x$ .

$\frac{19 \pm \sqrt{{(- 19)}^{2} - 4 \cdot (1 \cdot 88)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 19$ to the power of $2$ .

$x = \frac{19 \pm \sqrt{361 - 4 \cdot 1 \cdot 88}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 88$ .

Multiply $- 4$ by $1$ .

$x = \frac{19 \pm \sqrt{361 - 4 \cdot 88}}{2 \cdot 1}$

Multiply $- 4$ by $88$ .

$x = \frac{19 \pm \sqrt{361 - 352}}{2 \cdot 1}$

Subtract $352$ from $361$ .

$x = \frac{19 \pm \sqrt{9}}{2 \cdot 1}$

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

$x = \frac{19 \pm \sqrt{3^{2}}}{2 \cdot 1}$

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

$x = \frac{19 \pm 3}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{19 \pm 3}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 11, 8$