Solve Using the Quadratic Formula -9x^2+36x=38

$- 9 x^{2} + 36 x = 38$

Step 1

Subtract $38$ from both sides of the equation.

$- 9 x^{2} + 36 x - 38 = 0$

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 $a = - 9$ , $b = 36$ , and $c = - 38$ into the quadratic formula and solve for $x$ .

$\frac{- 36 \pm \sqrt{36^{2} - 4 \cdot (- 9 \cdot - 38)}}{2 \cdot - 9}$

Step 4

Simplify.

Simplify the numerator.

Raise $36$ to the power of $2$ .

$x = \frac{- 36 \pm \sqrt{1296 - 4 \cdot - 9 \cdot - 38}}{2 \cdot - 9}$

Multiply $- 4 \cdot - 9 \cdot - 38$ .

Multiply $- 4$ by $- 9$ .

$x = \frac{- 36 \pm \sqrt{1296 + 36 \cdot - 38}}{2 \cdot - 9}$

Multiply $36$ by $- 38$ .

$x = \frac{- 36 \pm \sqrt{1296 - 1368}}{2 \cdot - 9}$

Subtract $1368$ from $1296$ .

$x = \frac{- 36 \pm \sqrt{- 72}}{2 \cdot - 9}$

Rewrite $- 72$ as $- 1 (72)$ .

$x = \frac{- 36 \pm \sqrt{- 1 \cdot 72}}{2 \cdot - 9}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$x = \frac{- 36 \pm \sqrt{- 1} \cdot \sqrt{72}}{2 \cdot - 9}$

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

$x = \frac{- 36 \pm i \cdot \sqrt{72}}{2 \cdot - 9}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$x = \frac{- 36 \pm i \cdot \sqrt{36 (2)}}{2 \cdot - 9}$

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

$x = \frac{- 36 \pm i \cdot \sqrt{6^{2} \cdot 2}}{2 \cdot - 9}$

Pull terms out from under the radical.

$x = \frac{- 36 \pm i \cdot (6 \sqrt{2})}{2 \cdot - 9}$

Move $6$ to the left of $i$ .

$x = \frac{- 36 \pm 6 i \sqrt{2}}{2 \cdot - 9}$

Multiply $2$ by $- 9$ .

$x = \frac{- 36 \pm 6 i \sqrt{2}}{- 18}$

Simplify $\frac{- 36 \pm 6 i \sqrt{2}}{- 18}$ .

$x = \frac{6 \pm i \sqrt{2}}{3}$