Find the Roots (Zeros) x^2-8x-22=-10

$x^{2} - 8 x - 22 = - 10$

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

Add $10$ to both sides of the equation.

$x^{2} - 8 x - 22 + 10 = 0$

Add $- 22$ and $10$ .

$x^{2} - 8 x - 12 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = - 8$ , and $c = - 12$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot - 12)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 12}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 12}}{2 \cdot 1}$

Multiply $- 4$ by $- 12$ .

$x = \frac{8 \pm \sqrt{64 + 48}}{2 \cdot 1}$

Add $64$ and $48$ .

$x = \frac{8 \pm \sqrt{112}}{2 \cdot 1}$

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$x = \frac{8 \pm \sqrt{16 (7)}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{8 \pm \sqrt{4^{2} \cdot 7}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 4 \sqrt{7}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 4 \sqrt{7}}{2}$

Simplify $\frac{8 \pm 4 \sqrt{7}}{2}$ .

$x = 4 \pm 2 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$x = 4 \pm 2 \sqrt{7}$

Decimal Form:

$x = 9.29150262 \dots, - 1.29150262 \dots$