Solve Using the Quadratic Formula x^2+x=132

$x^{2} + x = 132$

Step 1

Subtract $132$ from both sides of the equation.

$x^{2} + x - 132 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 1$ , and $c = - 132$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot - 132)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 132}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 132$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 132}}{2 \cdot 1}$

Multiply $- 4$ by $- 132$ .

$x = \frac{- 1 \pm \sqrt{1 + 528}}{2 \cdot 1}$

Add $1$ and $528$ .

$x = \frac{- 1 \pm \sqrt{529}}{2 \cdot 1}$

Rewrite $529$ as $23^{2}$ .

$x = \frac{- 1 \pm \sqrt{23^{2}}}{2 \cdot 1}$

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

$x = \frac{- 1 \pm 23}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 1 \pm 23}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 11, - 12$