Solve Using the Quadratic Formula 4x^2+x+5=0

$4 x^{2} + x + 5 = 0$

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 $a = 4$ , $b = 1$ , and $c = 5$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

One to any power is one.

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

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

Multiply $- 4$ by $4$ .

$x = \frac{- 1 \pm \sqrt{1 - 16 \cdot 5}}{2 \cdot 4}$

Multiply $- 16$ by $5$ .

$x = \frac{- 1 \pm \sqrt{1 - 80}}{2 \cdot 4}$

Subtract $80$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 79}}{2 \cdot 4}$

Rewrite $- 79$ as $- 1 (79)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 79}}{2 \cdot 4}$

Rewrite $\sqrt{- 1 (79)}$ as $\sqrt{- 1} \cdot \sqrt{79}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{79}}{2 \cdot 4}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 1 \pm i \sqrt{79}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 1 \pm i \sqrt{79}}{8}$