Solve Using the Quadratic Formula x^2-9x=52

$x^{2} - 9 x = 52$

Step 1

Subtract $52$ from both sides of the equation.

$x^{2} - 9 x - 52 = 0$

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 $a = 1$ , $b = - 9$ , and $c = - 52$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (1 \cdot - 52)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot - 52}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 52$ .

Multiply $- 4$ by $1$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot - 52}}{2 \cdot 1}$

Multiply $- 4$ by $- 52$ .

$x = \frac{9 \pm \sqrt{81 + 208}}{2 \cdot 1}$

Add $81$ and $208$ .

$x = \frac{9 \pm \sqrt{289}}{2 \cdot 1}$

Rewrite $289$ as $17^{2}$ .

$x = \frac{9 \pm \sqrt{17^{2}}}{2 \cdot 1}$

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

$x = \frac{9 \pm 17}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{9 \pm 17}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 13, - 4$