Solve Using the Quadratic Formula x^2-10x-50=0

$x^{2} - 10 x - 50 = 0$

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 $a = 1$ , $b = - 10$ , and $c = - 50$ into the quadratic formula and solve for $x$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (1 \cdot - 50)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 10$ to the power of $2$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot 1 \cdot - 50}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 50$ .

Multiply $- 4$ by $1$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot - 50}}{2 \cdot 1}$

Multiply $- 4$ by $- 50$ .

$x = \frac{10 \pm \sqrt{100 + 200}}{2 \cdot 1}$

Add $100$ and $200$ .

$x = \frac{10 \pm \sqrt{300}}{2 \cdot 1}$

Rewrite $300$ as $10^{2} \cdot 3$ .

Factor $100$ out of $300$ .

$x = \frac{10 \pm \sqrt{100 (3)}}{2 \cdot 1}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{10 \pm \sqrt{10^{2} \cdot 3}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{10 \pm 10 \sqrt{3}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{10 \pm 10 \sqrt{3}}{2}$

Simplify $\frac{10 \pm 10 \sqrt{3}}{2}$ .

$x = 5 \pm 5 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 5 \pm 5 \sqrt{3}$

Decimal Form:

$x = 13.66025403 \dots, - 3.66025403 \dots$