Solve x^2+1/3+2=6

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

Solve for x

$$x = \frac{\sqrt{33}}{3} \approx 1.914854216$$

$$x = -\frac{\sqrt{33}}{3} \approx -1.914854216$$

Steps by Finding Square Root

Add \frac{1}{3} and 2 to get \frac{7}{3}.

$$x^{2}+\frac{7}{3}=6$$

Subtract \frac{7}{3} from both sides.

$$x^{2}=6-\frac{7}{3}$$

Subtract \frac{7}{3} from 6 to get \frac{11}{3}.

$$x^{2}=\frac{11}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{33}}{3} x=-\frac{\sqrt{33}}{3}$$

Steps Using the Quadratic Formula

Add \frac{1}{3} and 2 to get \frac{7}{3}.

$$x^{2}+\frac{7}{3}=6$$

Subtract 6 from both sides.

$$x^{2}+\frac{7}{3}-6=0$$

Subtract 6 from \frac{7}{3} to get -\frac{11}{3}.

$$x^{2}-\frac{11}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{11}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{11}{3}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{11}{3}\right)}}{2}$$

Multiply -4 times -\frac{11}{3}.

$$x=\frac{0±\sqrt{\frac{44}{3}}}{2}$$

Take the square root of \frac{44}{3}.

$$x=\frac{0±\frac{2\sqrt{33}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{33}}{3}}{2} when ± is plus.

$$x=\frac{\sqrt{33}}{3}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{33}}{3}}{2} when ± is minus.

$$x=-\frac{\sqrt{33}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{33}}{3} x=-\frac{\sqrt{33}}{3}$$