Solve 7q^2-8=0

$$7 q ^ { 2 } - 8 = 0$$

Solve for q

$$q = \frac{2 \sqrt{14}}{7} \approx 1.069044968$$

$$q = -\frac{2 \sqrt{14}}{7} \approx -1.069044968$$

Steps by Finding Square Root

Add 8 to both sides. Anything plus zero gives itself.

$$7q^{2}=8$$

Divide both sides by 7.

$$q^{2}=\frac{8}{7}$$

Take the square root of both sides of the equation.

$$q=\frac{2\sqrt{14}}{7} q=-\frac{2\sqrt{14}}{7}$$

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.

$$7q^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\times 7\left(-8\right)}}{2\times 7}$$

Square 0.

$$q=\frac{0±\sqrt{-4\times 7\left(-8\right)}}{2\times 7}$$

Multiply -4 times 7.

$$q=\frac{0±\sqrt{-28\left(-8\right)}}{2\times 7}$$

Multiply -28 times -8.

$$q=\frac{0±\sqrt{224}}{2\times 7}$$

Take the square root of 224.

$$q=\frac{0±4\sqrt{14}}{2\times 7}$$

Multiply 2 times 7.

$$q=\frac{0±4\sqrt{14}}{14}$$

Now solve the equation q=\frac{0±4\sqrt{14}}{14} when ± is plus.

$$q=\frac{2\sqrt{14}}{7}$$

Now solve the equation q=\frac{0±4\sqrt{14}}{14} when ± is minus.

$$q=-\frac{2\sqrt{14}}{7}$$

The equation is now solved.

$$q=\frac{2\sqrt{14}}{7} q=-\frac{2\sqrt{14}}{7}$$