Solve left(7xright)^2=4/9+1/3

$${ \left(7x \right) }^{ 2 } = \frac{ 4 }{ 9 } + \frac{ 1 }{ 3 }$$

Solve for x

$$x=\frac{\sqrt{7}}{21}\approx 0.125988158$$

$$x=-\frac{\sqrt{7}}{21}\approx -0.125988158$$

Steps by Finding Square Root

Expand \left(7x\right)^{2}.

$$7^{2}x^{2}=\frac{4}{9}+\frac{1}{3}$$

Calculate 7 to the power of 2 and get 49.

$$49x^{2}=\frac{4}{9}+\frac{1}{3}$$

Add \frac{4}{9} and \frac{1}{3} to get \frac{7}{9}.

$$49x^{2}=\frac{7}{9}$$

Divide both sides by 49.

$$x^{2}=\frac{\frac{7}{9}}{49}$$

Express \frac{\frac{7}{9}}{49} as a single fraction.

$$x^{2}=\frac{7}{9\times 49}$$

Multiply 9 and 49 to get 441.

$$x^{2}=\frac{7}{441}$$

Reduce the fraction \frac{7}{441} to lowest terms by extracting and canceling out 7.

$$x^{2}=\frac{1}{63}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{7}}{21} x=-\frac{\sqrt{7}}{21}$$

Steps Using the Quadratic Formula

Expand \left(7x\right)^{2}.

$$7^{2}x^{2}=\frac{4}{9}+\frac{1}{3}$$

Calculate 7 to the power of 2 and get 49.

$$49x^{2}=\frac{4}{9}+\frac{1}{3}$$

Add \frac{4}{9} and \frac{1}{3} to get \frac{7}{9}.

$$49x^{2}=\frac{7}{9}$$

Subtract \frac{7}{9} from both sides.

$$49x^{2}-\frac{7}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -\frac{7}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 49\left(-\frac{7}{9}\right)}}{2\times 49}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 49\left(-\frac{7}{9}\right)}}{2\times 49}$$

Multiply -4 times 49.

$$x=\frac{0±\sqrt{-196\left(-\frac{7}{9}\right)}}{2\times 49}$$

Multiply -196 times -\frac{7}{9}.

$$x=\frac{0±\sqrt{\frac{1372}{9}}}{2\times 49}$$

Take the square root of \frac{1372}{9}.

$$x=\frac{0±\frac{14\sqrt{7}}{3}}{2\times 49}$$

Multiply 2 times 49.

$$x=\frac{0±\frac{14\sqrt{7}}{3}}{98}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{7}}{3}}{98} when ± is plus.

$$x=\frac{\sqrt{7}}{21}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{7}}{3}}{98} when ± is minus.

$$x=-\frac{\sqrt{7}}{21}$$

The equation is now solved.

$$x=\frac{\sqrt{7}}{21} x=-\frac{\sqrt{7}}{21}$$