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

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

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 $a = 5$ , $b = - 10$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 5 \cdot - 2$ .

Multiply $- 4$ by $5$ .

$x = \frac{10 \pm \sqrt{100 - 20 \cdot - 2}}{2 \cdot 5}$

Multiply $- 20$ by $- 2$ .

$x = \frac{10 \pm \sqrt{100 + 40}}{2 \cdot 5}$

Add $100$ and $40$ .

$x = \frac{10 \pm \sqrt{140}}{2 \cdot 5}$

Rewrite $140$ as $2^{2} \cdot 35$ .

Factor $4$ out of $140$ .

$x = \frac{10 \pm \sqrt{4 (35)}}{2 \cdot 5}$

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

$x = \frac{10 \pm \sqrt{2^{2} \cdot 35}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{10 \pm 2 \sqrt{35}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{10 \pm 2 \sqrt{35}}{10}$

Simplify $\frac{10 \pm 2 \sqrt{35}}{10}$ .

$x = \frac{5 \pm \sqrt{35}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 \pm \sqrt{35}}{5}$

Decimal Form:

$x = 2.18321595 \dots, - 0.18321595 \dots$