Solve 3x^2-1=0

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

Solve for x

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps by Finding Square Root

Add 1 to both sides. Anything plus zero gives itself.

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

Divide both sides by 3.

$$x^{2}=\frac{1}{3}$$

Take the square root of both sides of the equation.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-1\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-1\right)}}{2\times 3}$$

Multiply -12 times -1.

$$x=\frac{0±\sqrt{12}}{2\times 3}$$

Take the square root of 12.

$$x=\frac{0±2\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{6} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{3}}{6} when ± is minus.

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

The equation is now solved.

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