Solve Using the Quadratic Formula 6x^2+1=13

$6 x^{2} + 1 = 13$

Step 1

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

Subtract $13$ from both sides of the equation.

$6 x^{2} + 1 - 13 = 0$

Subtract $13$ from $1$ .

$6 x^{2} - 12 = 0$

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 $a = 6$ , $b = 0$ , and $c = - 12$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (6 \cdot - 12)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 6 \cdot - 12}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 12$ .

Multiply $- 4$ by $6$ .

$x = \frac{0 \pm \sqrt{0 - 24 \cdot - 12}}{2 \cdot 6}$

Multiply $- 24$ by $- 12$ .

$x = \frac{0 \pm \sqrt{0 + 288}}{2 \cdot 6}$

Add $0$ and $288$ .

$x = \frac{0 \pm \sqrt{288}}{2 \cdot 6}$

Rewrite $288$ as $12^{2} \cdot 2$ .

Factor $144$ out of $288$ .

$x = \frac{0 \pm \sqrt{144 (2)}}{2 \cdot 6}$

Rewrite $144$ as $12^{2}$ .

$x = \frac{0 \pm \sqrt{12^{2} \cdot 2}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{0 \pm 12 \sqrt{2}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{0 \pm 12 \sqrt{2}}{12}$

Simplify $\frac{0 \pm 12 \sqrt{2}}{12}$ .

$x = \pm \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{2}$

Decimal Form:

$x = 1.41421356 \dots, - 1.41421356 \dots$