Solve 12x^2-16=0

$$12 { x }^{ 2 } -16=0$$

Solve for x

$$x = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$x = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Steps by Finding Square Root

Add 16 to both sides. Anything plus zero gives itself.

$$12x^{2}=16$$

Divide both sides by 12.

$$x^{2}=\frac{16}{12}$$

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{4}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{3}}{3} x=-\frac{2\sqrt{3}}{3}$$

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.

$$12x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-16\right)}}{2\times 12}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12\left(-16\right)}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{0±\sqrt{-48\left(-16\right)}}{2\times 12}$$

Multiply -48 times -16.

$$x=\frac{0±\sqrt{768}}{2\times 12}$$

Take the square root of 768.

$$x=\frac{0±16\sqrt{3}}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±16\sqrt{3}}{24}$$

Now solve the equation x=\frac{0±16\sqrt{3}}{24} when ± is plus.

$$x=\frac{2\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±16\sqrt{3}}{24} when ± is minus.

$$x=-\frac{2\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{3}}{3} x=-\frac{2\sqrt{3}}{3}$$