Solve 1/3x^2+4=49

$$\frac{ 1 }{ 3 } { x }^{ 2 } +4=49$$

Solve for x

$$x=3\sqrt{15}\approx 11.618950039$$

$$x=-3\sqrt{15}\approx -11.618950039$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$\frac{1}{3}x^{2}=49-4$$

Subtract 4 from 49 to get 45.

$$\frac{1}{3}x^{2}=45$$

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

$$x^{2}=45\times 3$$

Multiply 45 and 3 to get 135.

$$x^{2}=135$$

Take the square root of both sides of the equation.

$$x=3\sqrt{15} x=-3\sqrt{15}$$

Steps Using the Quadratic Formula

Subtract 49 from both sides.

$$\frac{1}{3}x^{2}+4-49=0$$

Subtract 49 from 4 to get -45.

$$\frac{1}{3}x^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{3} for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{3}\left(-45\right)}}{2\times \frac{1}{3}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{3}\left(-45\right)}}{2\times \frac{1}{3}}$$

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

$$x=\frac{0±\sqrt{-\frac{4}{3}\left(-45\right)}}{2\times \frac{1}{3}}$$

Multiply -\frac{4}{3} times -45.

$$x=\frac{0±\sqrt{60}}{2\times \frac{1}{3}}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2\times \frac{1}{3}}$$

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

$$x=\frac{0±2\sqrt{15}}{\frac{2}{3}}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{\frac{2}{3}} when ± is plus.

$$x=3\sqrt{15}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{\frac{2}{3}} when ± is minus.

$$x=-3\sqrt{15}$$

The equation is now solved.

$$x=3\sqrt{15} x=-3\sqrt{15}$$