Solve x^2=2^2+3^2-2*3*2+1/3

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

Solve for x

$$x = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$x = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 2 and get 9.

$$x^{2}=4+9-2\times 3\times 2+\frac{1}{3}$$

Add 4 and 9 to get 13.

$$x^{2}=13-2\times 3\times 2+\frac{1}{3}$$

Multiply 2 and 3 to get 6.

$$x^{2}=13-6\times 2+\frac{1}{3}$$

Multiply 6 and 2 to get 12.

$$x^{2}=13-12+\frac{1}{3}$$

Subtract 12 from 13 to get 1.

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

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

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 2 and get 9.

$$x^{2}=4+9-2\times 3\times 2+\frac{1}{3}$$

Add 4 and 9 to get 13.

$$x^{2}=13-2\times 3\times 2+\frac{1}{3}$$

Multiply 2 and 3 to get 6.

$$x^{2}=13-6\times 2+\frac{1}{3}$$

Multiply 6 and 2 to get 12.

$$x^{2}=13-12+\frac{1}{3}$$

Subtract 12 from 13 to get 1.

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

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

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

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

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

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

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

Square 0.

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

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

$$x=\frac{0±\sqrt{\frac{16}{3}}}{2}$$

Take the square root of \frac{16}{3}.

$$x=\frac{0±\frac{4\sqrt{3}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{3}}{3}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{4\sqrt{3}}{3}}{2} when ± is minus.

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

The equation is now solved.

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