Solve Using the Quadratic Formula x^2+24x+144=0

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

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 $a = 1$ , $b = 24$ , and $c = 144$ into the quadratic formula and solve for $x$ .

$\frac{- 24 \pm \sqrt{24^{2} - 4 \cdot (1 \cdot 144)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 1 \cdot 144}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 144$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 144}}{2 \cdot 1}$

Multiply $- 4$ by $144$ .

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

Subtract $576$ from $576$ .

$x = \frac{- 24 \pm \sqrt{0}}{2 \cdot 1}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{- 24 \pm \sqrt{0^{2}}}{2 \cdot 1}$

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

$x = \frac{- 24 \pm 0}{2 \cdot 1}$

$- 24$ plus or minus $0$ is $- 24$ .

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

Multiply $2$ by $1$ .

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

Divide $- 24$ by $2$ .

$x = - 12$

Step 4

The final answer is the combination of both solutions.

$x = - 12$ Double roots