Solve Using the Quadratic Formula (3x+2)^2-49=0

${(3 x + 2)}^{2} - 49 = 0$

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 $a = 9$ , $b = 12$ , and $c = - 45$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (9 \cdot - 45)}}{2 \cdot 9}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 9 \cdot - 45}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 45$ .

Multiply $- 4$ by $9$ .

$x = \frac{- 12 \pm \sqrt{144 - 36 \cdot - 45}}{2 \cdot 9}$

Multiply $- 36$ by $- 45$ .

$x = \frac{- 12 \pm \sqrt{144 + 1620}}{2 \cdot 9}$

Add $144$ and $1620$ .

$x = \frac{- 12 \pm \sqrt{1764}}{2 \cdot 9}$

Rewrite $1764$ as $42^{2}$ .

$x = \frac{- 12 \pm \sqrt{42^{2}}}{2 \cdot 9}$

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

$x = \frac{- 12 \pm 42}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{- 12 \pm 42}{18}$

Simplify $\frac{- 12 \pm 42}{18}$ .

$x = \frac{- 2 \pm 7}{3}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{5}{3}, - 3$