Solve Using the Quadratic Formula x^2+10x-1=0

$x^{2} + 10 x - 1 = 0$

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 $c = - 1$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 1$ .

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

Add $100$ and $4$ .

$x = \frac{- 10 \pm \sqrt{104}}{2 \cdot 1}$

Rewrite $104$ as $2^{2} \cdot 26$ .

Factor $4$ out of $104$ .

$x = \frac{- 10 \pm \sqrt{4 (26)}}{2 \cdot 1}$

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

$x = \frac{- 10 \pm \sqrt{2^{2} \cdot 26}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 10 \pm 2 \sqrt{26}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 10 \pm 2 \sqrt{26}}{2}$

Simplify $\frac{- 10 \pm 2 \sqrt{26}}{2}$ .

$x = - 5 \pm \sqrt{26}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 5 \pm \sqrt{26}$

Decimal Form:

$x = 0.09901951 \dots, - 10.09901951 \dots$