Solve Using the Quadratic Formula x^2-18x+77=0

$x^{2} - 18 x + 77 = 0$

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 $a = 1$ , $b = - 18$ , and $c = 77$ into the quadratic formula and solve for $x$ .

$\frac{18 \pm \sqrt{{(- 18)}^{2} - 4 \cdot (1 \cdot 77)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 18$ to the power of $2$ .

$x = \frac{18 \pm \sqrt{324 - 4 \cdot 1 \cdot 77}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{18 \pm \sqrt{324 - 4 \cdot 77}}{2 \cdot 1}$

Multiply $- 4$ by $77$ .

$x = \frac{18 \pm \sqrt{324 - 308}}{2 \cdot 1}$

Subtract $308$ from $324$ .

$x = \frac{18 \pm \sqrt{16}}{2 \cdot 1}$

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

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

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

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

Multiply $2$ by $1$ .

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

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

$x = 9 \pm 2$

Step 4

The final answer is the combination of both solutions.

$x = 11, 7$