Solve 7v^2-7=-86

$$7 v ^ { 2 } - 7 = - 86$$

Solve for v

$$v=-\frac{\sqrt{553}i}{7}\approx -0-3.359421719i$$

$$v=\frac{\sqrt{553}i}{7}\approx 3.359421719i$$

Steps by Finding Square Root

Add 7 to both sides.

$$7v^{2}=-86+7$$

Add -86 and 7 to get -79.

$$7v^{2}=-79$$

Divide both sides by 7.

$$v^{2}=-\frac{79}{7}$$

The equation is now solved.

$$v=\frac{\sqrt{553}i}{7} v=-\frac{\sqrt{553}i}{7}$$

Steps Using the Quadratic Formula

Add 86 to both sides.

$$7v^{2}-7+86=0$$

Add -7 and 86 to get 79.

$$7v^{2}+79=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and 79 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times 7\times 79}}{2\times 7}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times 7\times 79}}{2\times 7}$$

Multiply -4 times 7.

$$v=\frac{0±\sqrt{-28\times 79}}{2\times 7}$$

Multiply -28 times 79.

$$v=\frac{0±\sqrt{-2212}}{2\times 7}$$

Take the square root of -2212.

$$v=\frac{0±2\sqrt{553}i}{2\times 7}$$

Multiply 2 times 7.

$$v=\frac{0±2\sqrt{553}i}{14}$$

Now solve the equation v=\frac{0±2\sqrt{553}i}{14} when ± is plus.

$$v=\frac{\sqrt{553}i}{7}$$

Now solve the equation v=\frac{0±2\sqrt{553}i}{14} when ± is minus.

$$v=-\frac{\sqrt{553}i}{7}$$

The equation is now solved.

$$v=\frac{\sqrt{553}i}{7} v=-\frac{\sqrt{553}i}{7}$$