Solve Using the Quadratic Formula x^2+16x+51=0

$x^{2} + 16 x + 51 = 0$

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 $a = 1$ , $b = 16$ , and $c = 51$ into the quadratic formula and solve for $x$ .

$\frac{- 16 \pm \sqrt{16^{2} - 4 \cdot (1 \cdot 51)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $16$ to the power of $2$ .

$x = \frac{- 16 \pm \sqrt{256 - 4 \cdot 1 \cdot 51}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 51$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 16 \pm \sqrt{256 - 4 \cdot 51}}{2 \cdot 1}$

Multiply $- 4$ by $51$ .

$x = \frac{- 16 \pm \sqrt{256 - 204}}{2 \cdot 1}$

Subtract $204$ from $256$ .

$x = \frac{- 16 \pm \sqrt{52}}{2 \cdot 1}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$x = \frac{- 16 \pm \sqrt{4 (13)}}{2 \cdot 1}$

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

$x = \frac{- 16 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 16 \pm 2 \sqrt{13}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 16 \pm 2 \sqrt{13}}{2}$

Simplify $\frac{- 16 \pm 2 \sqrt{13}}{2}$ .

$x = - 8 \pm \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 8 \pm \sqrt{13}$

Decimal Form:

$x = - 4.39444872 \dots, - 11.60555127 \dots$