Solve x^2-3/7=0

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

Solve for x

$$x=\frac{\sqrt{21}}{7}\approx 0.654653671$$

$$x=-\frac{\sqrt{21}}{7}\approx -0.654653671$$

Steps by Finding Square Root

Add \frac{3}{7} to both sides. Anything plus zero gives itself.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3}{7} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{7}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3}{7}\right)}}{2}$$

Multiply -4 times -\frac{3}{7}.

$$x=\frac{0±\sqrt{\frac{12}{7}}}{2}$$

Take the square root of \frac{12}{7}.

$$x=\frac{0±\frac{2\sqrt{21}}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{21}}{7}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{2\sqrt{21}}{7}}{2} when ± is minus.

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

The equation is now solved.

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