Solve Using the Quadratic Formula 4x^2+8x-1=0

$4 x^{2} + 8 x - 1 = 0$

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 $a = 4$ , $b = 8$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (4 \cdot - 1)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $8$ to the power of $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 4 \cdot - 1}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{- 8 \pm \sqrt{64 - 16 \cdot - 1}}{2 \cdot 4}$

Multiply $- 16$ by $- 1$ .

$x = \frac{- 8 \pm \sqrt{64 + 16}}{2 \cdot 4}$

Add $64$ and $16$ .

$x = \frac{- 8 \pm \sqrt{80}}{2 \cdot 4}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$x = \frac{- 8 \pm \sqrt{16 (5)}}{2 \cdot 4}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{- 8 \pm \sqrt{4^{2} \cdot 5}}{2 \cdot 4}$

Pull terms out from under the radical.

$x = \frac{- 8 \pm 4 \sqrt{5}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 8 \pm 4 \sqrt{5}}{8}$

Simplify $\frac{- 8 \pm 4 \sqrt{5}}{8}$ .

$x = \frac{- 2 \pm \sqrt{5}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 2 \pm \sqrt{5}}{2}$

Decimal Form:

$x = 0.11803398 \dots, - 2.11803398 \dots$