Solve for x x^2-10x-4=0

$x^{2} - 10 x - 4 = 0$

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 $c = - 4$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 4$ .

$x = \frac{10 \pm \sqrt{100 + 16}}{2 \cdot 1}$

Add $100$ and $16$ .

$x = \frac{10 \pm \sqrt{116}}{2 \cdot 1}$

Rewrite $116$ as $2^{2} \cdot 29$ .

Factor $4$ out of $116$ .

$x = \frac{10 \pm \sqrt{4 (29)}}{2 \cdot 1}$

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

$x = \frac{10 \pm \sqrt{2^{2} \cdot 29}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{10 \pm 2 \sqrt{29}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{10 \pm 2 \sqrt{29}}{2}$

Simplify $\frac{10 \pm 2 \sqrt{29}}{2}$ .

$x = 5 \pm \sqrt{29}$

Step 4

The final answer is the combination of both solutions.

$x = 5 + \sqrt{29}, 5 - \sqrt{29}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 5 + \sqrt{29}, 5 - \sqrt{29}$

Decimal Form:

$x = 10.38516480 \dots, - 0.38516480 \dots$