Solve Using the Quadratic Formula 3w^2-14=13

$3 w^{2} - 14 = 13$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $13$ from both sides of the equation.

$3 w^{2} - 14 - 13 = 0$

Subtract $13$ from $- 14$ .

$3 w^{2} - 27 = 0$

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 $a = 3$ , $b = 0$ , and $c = - 27$ into the quadratic formula and solve for $w$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 27)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$w = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 27}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 27$ .

Multiply $- 4$ by $3$ .

$w = \frac{0 \pm \sqrt{0 - 12 \cdot - 27}}{2 \cdot 3}$

Multiply $- 12$ by $- 27$ .

$w = \frac{0 \pm \sqrt{0 + 324}}{2 \cdot 3}$

Add $0$ and $324$ .

$w = \frac{0 \pm \sqrt{324}}{2 \cdot 3}$

Rewrite $324$ as $18^{2}$ .

$w = \frac{0 \pm \sqrt{18^{2}}}{2 \cdot 3}$

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

$w = \frac{0 \pm 18}{2 \cdot 3}$

Multiply $2$ by $3$ .

$w = \frac{0 \pm 18}{6}$

Simplify $\frac{0 \pm 18}{6}$ .

$w = \pm 3$

Step 5

The final answer is the combination of both solutions.

$w = 3, - 3$