Solve 7/3x^2=3/7

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

Solve for x

$$x=\frac{3}{7}\approx 0.428571429$$

$$x=-\frac{3}{7}\approx -0.428571429$$

Steps Using Difference of Squares

Multiply both sides by \frac{3}{7}, the reciprocal of \frac{7}{3}.

$$x^{2}=\frac{3}{7}\times \frac{3}{7}$$

Multiply \frac{3}{7} and \frac{3}{7} to get \frac{9}{49}.

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

Subtract \frac{9}{49} from both sides.

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

Multiply both sides by 49.

$$49x^{2}-9=0$$

Consider 49x^{2}-9. Rewrite 49x^{2}-9 as \left(7x\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7x-3\right)\left(7x+3\right)=0$$

To find equation solutions, solve 7x-3=0 and 7x+3=0.

$$x=\frac{3}{7} x=-\frac{3}{7}$$

Steps by Finding Square Root

Multiply both sides by \frac{3}{7}, the reciprocal of \frac{7}{3}.

$$x^{2}=\frac{3}{7}\times \frac{3}{7}$$

Multiply \frac{3}{7} and \frac{3}{7} to get \frac{9}{49}.

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

Take the square root of both sides of the equation.

$$x=\frac{3}{7} x=-\frac{3}{7}$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{3}{7}, the reciprocal of \frac{7}{3}.

$$x^{2}=\frac{3}{7}\times \frac{3}{7}$$

Multiply \frac{3}{7} and \frac{3}{7} to get \frac{9}{49}.

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

Subtract \frac{9}{49} from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -\frac{9}{49}.

$$x=\frac{0±\sqrt{\frac{36}{49}}}{2}$$

Take the square root of \frac{36}{49}.

$$x=\frac{0±\frac{6}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{6}{7}}{2} when ± is plus.

$$x=\frac{3}{7}$$

Now solve the equation x=\frac{0±\frac{6}{7}}{2} when ± is minus.

$$x=-\frac{3}{7}$$

The equation is now solved.

$$x=\frac{3}{7} x=-\frac{3}{7}$$