Solve Using the Quadratic Formula x^2+24x+144=9

$x^{2} + 24 x + 144 = 9$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $9$ from both sides of the equation.

$x^{2} + 24 x + 144 - 9 = 0$

Subtract $9$ from $144$ .

$x^{2} + 24 x + 135 = 0$

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 $a = 1$ , $b = 24$ , and $c = 135$ into the quadratic formula and solve for $x$ .

$\frac{- 24 \pm \sqrt{24^{2} - 4 \cdot (1 \cdot 135)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $24$ to the power of $2$ .

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 1 \cdot 135}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 135$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 135}}{2 \cdot 1}$

Multiply $- 4$ by $135$ .

$x = \frac{- 24 \pm \sqrt{576 - 540}}{2 \cdot 1}$

Subtract $540$ from $576$ .

$x = \frac{- 24 \pm \sqrt{36}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 24 \pm \sqrt{6^{2}}}{2 \cdot 1}$

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

$x = \frac{- 24 \pm 6}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 24 \pm 6}{2}$

Simplify $\frac{- 24 \pm 6}{2}$ .

$x = - 12 \pm 3$

Step 5

The final answer is the combination of both solutions.

$x = - 9, - 15$