Solve Using the Quadratic Formula X^2-12X+72=0

$X^{2} - 12 X + 72 = 0$

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 $a = 1$ , $b = - 12$ , and $c = 72$ into the quadratic formula and solve for $X$ .

$\frac{12 \pm \sqrt{{(- 12)}^{2} - 4 \cdot (1 \cdot 72)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 12$ to the power of $2$ .

$X = \frac{12 \pm \sqrt{144 - 4 \cdot 1 \cdot 72}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 72$ .

Multiply $- 4$ by $1$ .

$X = \frac{12 \pm \sqrt{144 - 4 \cdot 72}}{2 \cdot 1}$

Multiply $- 4$ by $72$ .

$X = \frac{12 \pm \sqrt{144 - 288}}{2 \cdot 1}$

Subtract $288$ from $144$ .

$X = \frac{12 \pm \sqrt{- 144}}{2 \cdot 1}$

Rewrite $- 144$ as $- 1 (144)$ .

$X = \frac{12 \pm \sqrt{- 1 \cdot 144}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (144)}$ as $\sqrt{- 1} \cdot \sqrt{144}$ .

$X = \frac{12 \pm \sqrt{- 1} \cdot \sqrt{144}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$X = \frac{12 \pm i \cdot \sqrt{144}}{2 \cdot 1}$

Rewrite $144$ as $12^{2}$ .

$X = \frac{12 \pm i \cdot \sqrt{12^{2}}}{2 \cdot 1}$

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

$X = \frac{12 \pm i \cdot 12}{2 \cdot 1}$

Move $12$ to the left of $i$ .

$X = \frac{12 \pm 12 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$X = \frac{12 \pm 12 i}{2}$

Simplify $\frac{12 \pm 12 i}{2}$ .

$X = 6 \pm 6 i$