Solve for x 9x^2+12x=-6

$9 x^{2} + 12 x = - 6$

Add $6$ to both sides of the equation.

$9 x^{2} + 12 x + 6 = 0$

Factor $3$ out of $9 x^{2} + 12 x + 6$ .

Factor $3$ out of $9 x^{2}$ .

$3 (3 x^{2}) + 12 x + 6 = 0$

Factor $3$ out of $12 x$ .

$3 (3 x^{2}) + 3 (4 x) + 6 = 0$

Factor $3$ out of $6$ .

$3 (3 x^{2}) + 3 (4 x) + 3 (2) = 0$

Factor $3$ out of $3 (3 x^{2}) + 3 (4 x)$ .

$3 (3 x^{2} + 4 x) + 3 (2) = 0$

Factor $3$ out of $3 (3 x^{2} + 4 x) + 3 (2)$ .

$3 (3 x^{2} + 4 x + 2) = 0$

Divide each term in $3 (3 x^{2} + 4 x + 2) = 0$ by $3$ and simplify.

Divide each term in $3 (3 x^{2} + 4 x + 2) = 0$ by $3$ .

$\frac{3 (3 x^{2} + 4 x + 2)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (3 x^{2} + 4 x + 2)}{3} = \frac{0}{3}$

Divide $3 x^{2} + 4 x + 2$ by $1$ .

$3 x^{2} + 4 x + 2 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$3 x^{2} + 4 x + 2 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = 4$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (3 \cdot 2)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 3 \cdot 2}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{- 4 \pm \sqrt{16 - 12 \cdot 2}}{2 \cdot 3}$

Multiply $- 12$ by $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 24}}{2 \cdot 3}$

Subtract $24$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 8}}{2 \cdot 3}$

Rewrite $- 8$ as $- 1 (8)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 8}}{2 \cdot 3}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{8}}{2 \cdot 3}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{8}}{2 \cdot 3}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (2)}}{2 \cdot 3}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 2}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{2})}{2 \cdot 3}$

Move $2$ to the left of $i$ .

$x = \frac{- 4 \pm 2 i \sqrt{2}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 4 \pm 2 i \sqrt{2}}{6}$

Simplify $\frac{- 4 \pm 2 i \sqrt{2}}{6}$ .

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

The final answer is the combination of both solutions.

$x = - \frac{2 - i \sqrt{2}}{3}, - \frac{2 + i \sqrt{2}}{3}$

Solve for x 9x^2+12x=-6

Related Questions

Support LCMGCF.com by disabling your adblocker.