Solve 2(1-3x^2)=0

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

Solve for x

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

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

Steps by Finding Square Root

Divide both sides by 2. Zero divided by any non-zero number gives zero.

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

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -3.

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

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

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

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

Divide both sides by 2. Zero divided by any non-zero number gives zero.

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

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}.

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

Square 0.

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

Multiply -4 times -3.

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

Take the square root of 12.

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

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.

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