Solve 1/3(x^2-1/2)=1/4

$$\frac { 1 } { 3 } ( x ^ { 2 } - \frac { 1 } { 2 } ) = \frac { 1 } { 4 }$$

Solve for x

$$x = \frac{\sqrt{5}}{2} \approx 1.118033989$$

$$x = -\frac{\sqrt{5}}{2} \approx -1.118033989$$

Steps by Finding Square Root

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$x^{2}-\frac{1}{2}=\frac{1}{4}\times 3$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$x^{2}-\frac{1}{2}=\frac{3}{4}$$

Add \frac{1}{2} to both sides.

$$x^{2}=\frac{3}{4}+\frac{1}{2}$$

Add \frac{3}{4} and \frac{1}{2} to get \frac{5}{4}.

$$x^{2}=\frac{5}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{5}}{2} x=-\frac{\sqrt{5}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$x^{2}-\frac{1}{2}=\frac{1}{4}\times 3$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$x^{2}-\frac{1}{2}=\frac{3}{4}$$

Subtract \frac{3}{4} from both sides.

$$x^{2}-\frac{1}{2}-\frac{3}{4}=0$$

Subtract \frac{3}{4} from -\frac{1}{2} to get -\frac{5}{4}.

$$x^{2}-\frac{5}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{5}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{5}{4}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{5}{4}\right)}}{2}$$

Multiply -4 times -\frac{5}{4}.

$$x=\frac{0±\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±\sqrt{5}}{2} when ± is plus.

$$x=\frac{\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±\sqrt{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{5}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{5}}{2} x=-\frac{\sqrt{5}}{2}$$