Solve Using the Quadratic Formula 2x^2+24x+72=0

$2 x^{2} + 24 x + 72 = 0$

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 $a = 2$ , $b = 24$ , and $c = 72$ into the quadratic formula and solve for $x$ .

$\frac{- 24 \pm \sqrt{24^{2} - 4 \cdot (2 \cdot 72)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 2 \cdot 72}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 72$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 24 \pm \sqrt{576 - 8 \cdot 72}}{2 \cdot 2}$

Multiply $- 8$ by $72$ .

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

Subtract $576$ from $576$ .

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

$x = \frac{- 24}{4}$

Divide $- 24$ by $4$ .

$x = - 6$

Step 4

The final answer is the combination of both solutions.

$x = - 6$ Double roots