Solve 7w^2-3=0

$$7 w ^ { 2 } - 3 = 0$$

Solve for w

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

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

Steps by Finding Square Root

Add 3 to both sides. Anything plus zero gives itself.

$$7w^{2}=3$$

Divide both sides by 7.

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

Take the square root of both sides of the equation.

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

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.

$$7w^{2}-3=0$$

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

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

Square 0.

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

Multiply -4 times 7.

$$w=\frac{0±\sqrt{-28\left(-3\right)}}{2\times 7}$$

Multiply -28 times -3.

$$w=\frac{0±\sqrt{84}}{2\times 7}$$

Take the square root of 84.

$$w=\frac{0±2\sqrt{21}}{2\times 7}$$

Multiply 2 times 7.

$$w=\frac{0±2\sqrt{21}}{14}$$

Now solve the equation w=\frac{0±2\sqrt{21}}{14} when ± is plus.

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

Now solve the equation w=\frac{0±2\sqrt{21}}{14} when ± is minus.

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

The equation is now solved.

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