Solve 1/3x^2-1=5

$$\frac { 1 } { 3 } x ^ { 2 } - 1 = 5$$

Solve for x

$$x=3\sqrt{2}\approx 4.242640687$$

$$x=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Add 1 to both sides.

$$\frac{1}{3}x^{2}=5+1$$

Add 5 and 1 to get 6.

$$\frac{1}{3}x^{2}=6$$

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

$$x^{2}=6\times 3$$

Multiply 6 and 3 to get 18.

$$x^{2}=18$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 5 from both sides.

$$\frac{1}{3}x^{2}-1-5=0$$

Subtract 5 from -1 to get -6.

$$\frac{1}{3}x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{3} for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{3}\left(-6\right)}}{2\times \frac{1}{3}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{3}\left(-6\right)}}{2\times \frac{1}{3}}$$

Multiply -4 times \frac{1}{3}.

$$x=\frac{0±\sqrt{-\frac{4}{3}\left(-6\right)}}{2\times \frac{1}{3}}$$

Multiply -\frac{4}{3} times -6.

$$x=\frac{0±\sqrt{8}}{2\times \frac{1}{3}}$$

Take the square root of 8.

$$x=\frac{0±2\sqrt{2}}{2\times \frac{1}{3}}$$

Multiply 2 times \frac{1}{3}.

$$x=\frac{0±2\sqrt{2}}{\frac{2}{3}}$$

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

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

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

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

The equation is now solved.

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