Solve Using the Quadratic Formula 3x^2-1=47

$3 x^{2} - 1 = 47$

Step 1

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

Subtract $47$ from both sides of the equation.

$3 x^{2} - 1 - 47 = 0$

Subtract $47$ from $- 1$ .

$3 x^{2} - 48 = 0$

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 $c = - 48$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 48)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 48}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 48$ .

Multiply $- 4$ by $3$ .

$x = \frac{0 \pm \sqrt{0 - 12 \cdot - 48}}{2 \cdot 3}$

Multiply $- 12$ by $- 48$ .

$x = \frac{0 \pm \sqrt{0 + 576}}{2 \cdot 3}$

Add $0$ and $576$ .

$x = \frac{0 \pm \sqrt{576}}{2 \cdot 3}$

Rewrite $576$ as $24^{2}$ .

$x = \frac{0 \pm \sqrt{24^{2}}}{2 \cdot 3}$

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

$x = \frac{0 \pm 24}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{0 \pm 24}{6}$

Simplify $\frac{0 \pm 24}{6}$ .

$x = \pm 4$

Step 5

The final answer is the combination of both solutions.

$x = 4, - 4$