Solve Using the Quadratic Formula x^2-4x-77=0

$x^{2} - 4 x - 77 = 0$

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 $a = 1$ , $b = - 4$ , and $c = - 77$ into the quadratic formula and solve for $x$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (1 \cdot - 77)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 4$ to the power of $2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 77}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 77$ .

Multiply $- 4$ by $1$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot - 77}}{2 \cdot 1}$

Multiply $- 4$ by $- 77$ .

$x = \frac{4 \pm \sqrt{16 + 308}}{2 \cdot 1}$

Add $16$ and $308$ .

$x = \frac{4 \pm \sqrt{324}}{2 \cdot 1}$

Rewrite $324$ as $18^{2}$ .

$x = \frac{4 \pm \sqrt{18^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{4 \pm 18}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{4 \pm 18}{2}$

Simplify $\frac{4 \pm 18}{2}$ .

$x = 2 \pm 9$

Step 4

The final answer is the combination of both solutions.

$x = 11, - 7$