Solve 21x^2-7=0

$$21 { x }^{ 2 } -7=0$$

Solve for x

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps by Finding Square Root

Add 7 to both sides. Anything plus zero gives itself.

$$21x^{2}=7$$

Divide both sides by 21.

$$x^{2}=\frac{7}{21}$$

Reduce the fraction \frac{7}{21} to lowest terms by extracting and canceling out 7.

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

Take the square root of both sides of the equation.

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

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.

$$21x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 21 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 21\left(-7\right)}}{2\times 21}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 21\left(-7\right)}}{2\times 21}$$

Multiply -4 times 21.

$$x=\frac{0±\sqrt{-84\left(-7\right)}}{2\times 21}$$

Multiply -84 times -7.

$$x=\frac{0±\sqrt{588}}{2\times 21}$$

Take the square root of 588.

$$x=\frac{0±14\sqrt{3}}{2\times 21}$$

Multiply 2 times 21.

$$x=\frac{0±14\sqrt{3}}{42}$$

Now solve the equation x=\frac{0±14\sqrt{3}}{42} when ± is plus.

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

Now solve the equation x=\frac{0±14\sqrt{3}}{42} when ± is minus.

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

The equation is now solved.

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