Solve 6x^2-46=0

$$6 x ^ { 2 } - 46 = 0$$

Solve for x

$$x = \frac{\sqrt{69}}{3} \approx 2.768874621$$

$$x = -\frac{\sqrt{69}}{3} \approx -2.768874621$$

Steps by Finding Square Root

Add 46 to both sides. Anything plus zero gives itself.

$$6x^{2}=46$$

Divide both sides by 6.

$$x^{2}=\frac{46}{6}$$

Reduce the fraction \frac{46}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{23}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{69}}{3} x=-\frac{\sqrt{69}}{3}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$6x^{2}-46=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -46 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-46\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-46\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-46\right)}}{2\times 6}$$

Multiply -24 times -46.

$$x=\frac{0±\sqrt{1104}}{2\times 6}$$

Take the square root of 1104.

$$x=\frac{0±4\sqrt{69}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±4\sqrt{69}}{12}$$

Now solve the equation x=\frac{0±4\sqrt{69}}{12} when ± is plus.

$$x=\frac{\sqrt{69}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{69}}{12} when ± is minus.

$$x=-\frac{\sqrt{69}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{69}}{3} x=-\frac{\sqrt{69}}{3}$$