Solve x^2-2/3x*x=2

$$x ^ { 2 } - \frac { 2 } { 3 } x \cdot x = 2$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

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

Combine x^{2} and -\frac{2}{3}x^{2} to get \frac{1}{3}x^{2}.

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

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

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

Multiply 2 and 3 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

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

Combine x^{2} and -\frac{2}{3}x^{2} to get \frac{1}{3}x^{2}.

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

Subtract 2 from both sides.

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

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

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

Square 0.

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

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

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

Multiply -\frac{4}{3} times -2.

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

Take the square root of \frac{8}{3}.

$$x=\frac{0±\frac{2\sqrt{6}}{3}}{2\times \frac{1}{3}}$$

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

$$x=\frac{0±\frac{2\sqrt{6}}{3}}{\frac{2}{3}}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{6}}{3}}{\frac{2}{3}} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{6}}{3}}{\frac{2}{3}} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$