Solve Using the Quadratic Formula x^2+10x-5=0

$x^{2} + 10 x - 5 = 0$

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 $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (1 \cdot - 5)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 1 \cdot - 5}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 5$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot - 5}}{2 \cdot 1}$

Multiply $- 4$ by $- 5$ .

$x = \frac{- 10 \pm \sqrt{100 + 20}}{2 \cdot 1}$

Add $100$ and $20$ .

$x = \frac{- 10 \pm \sqrt{120}}{2 \cdot 1}$

Rewrite $120$ as $2^{2} \cdot 30$ .

Factor $4$ out of $120$ .

$x = \frac{- 10 \pm \sqrt{4 (30)}}{2 \cdot 1}$

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

$x = \frac{- 10 \pm \sqrt{2^{2} \cdot 30}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 10 \pm 2 \sqrt{30}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 10 \pm 2 \sqrt{30}}{2}$

Simplify $\frac{- 10 \pm 2 \sqrt{30}}{2}$ .

$x = - 5 \pm \sqrt{30}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 5 \pm \sqrt{30}$

Decimal Form:

$x = 0.47722557 \dots, - 10.47722557 \dots$