Solve 60x^2-12=0

$$60 x ^ { 2 } - 12 = 0$$

Solve for x

$$x=\frac{\sqrt{5}}{5}\approx 0.447213595$$

$$x=-\frac{\sqrt{5}}{5}\approx -0.447213595$$

Steps by Finding Square Root

Add 12 to both sides. Anything plus zero gives itself.

$$60x^{2}=12$$

Divide both sides by 60.

$$x^{2}=\frac{12}{60}$$

Reduce the fraction \frac{12}{60} to lowest terms by extracting and canceling out 12.

$$x^{2}=\frac{1}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{5}}{5} x=-\frac{\sqrt{5}}{5}$$

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.

$$60x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 60 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 60\left(-12\right)}}{2\times 60}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 60\left(-12\right)}}{2\times 60}$$

Multiply -4 times 60.

$$x=\frac{0±\sqrt{-240\left(-12\right)}}{2\times 60}$$

Multiply -240 times -12.

$$x=\frac{0±\sqrt{2880}}{2\times 60}$$

Take the square root of 2880.

$$x=\frac{0±24\sqrt{5}}{2\times 60}$$

Multiply 2 times 60.

$$x=\frac{0±24\sqrt{5}}{120}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{120} when ± is plus.

$$x=\frac{\sqrt{5}}{5}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{120} when ± is minus.

$$x=-\frac{\sqrt{5}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{5}}{5} x=-\frac{\sqrt{5}}{5}$$