Solve 100=1/160V^2+1/3/6

$$100 = \frac { 1 } { 160 } V ^ { 2 } + \frac { 1 } { 3 / 6 }$$

Solve for V

$$V=56\sqrt{5}\approx 125.21980674$$

$$V=-56\sqrt{5}\approx -125.21980674$$

Steps by Finding Square Root

Divide 1 by \frac{3}{6} by multiplying 1 by the reciprocal of \frac{3}{6}.

$$100=\frac{1}{160}V^{2}+\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$100=\frac{1}{160}V^{2}+2$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{160}V^{2}+2=100$$

Subtract 2 from both sides.

$$\frac{1}{160}V^{2}=100-2$$

Subtract 2 from 100 to get 98.

$$\frac{1}{160}V^{2}=98$$

Multiply both sides by 160, the reciprocal of \frac{1}{160}.

$$V^{2}=98\times 160$$

Multiply 98 and 160 to get 15680.

$$V^{2}=15680$$

Take the square root of both sides of the equation.

$$V=56\sqrt{5} V=-56\sqrt{5}$$

Steps Using the Quadratic Formula

Divide 1 by \frac{3}{6} by multiplying 1 by the reciprocal of \frac{3}{6}.

$$100=\frac{1}{160}V^{2}+\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$100=\frac{1}{160}V^{2}+2$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{160}V^{2}+2=100$$

Subtract 100 from both sides.

$$\frac{1}{160}V^{2}+2-100=0$$

Subtract 100 from 2 to get -98.

$$\frac{1}{160}V^{2}-98=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{160} for a, 0 for b, and -98 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$V=\frac{0±\sqrt{0^{2}-4\times \frac{1}{160}\left(-98\right)}}{2\times \frac{1}{160}}$$

Square 0.

$$V=\frac{0±\sqrt{-4\times \frac{1}{160}\left(-98\right)}}{2\times \frac{1}{160}}$$

Multiply -4 times \frac{1}{160}.

$$V=\frac{0±\sqrt{-\frac{1}{40}\left(-98\right)}}{2\times \frac{1}{160}}$$

Multiply -\frac{1}{40} times -98.

$$V=\frac{0±\sqrt{\frac{49}{20}}}{2\times \frac{1}{160}}$$

Take the square root of \frac{49}{20}.

$$V=\frac{0±\frac{7\sqrt{5}}{10}}{2\times \frac{1}{160}}$$

Multiply 2 times \frac{1}{160}.

$$V=\frac{0±\frac{7\sqrt{5}}{10}}{\frac{1}{80}}$$

Now solve the equation V=\frac{0±\frac{7\sqrt{5}}{10}}{\frac{1}{80}} when ± is plus.

$$V=56\sqrt{5}$$

Now solve the equation V=\frac{0±\frac{7\sqrt{5}}{10}}{\frac{1}{80}} when ± is minus.

$$V=-56\sqrt{5}$$

The equation is now solved.

$$V=56\sqrt{5} V=-56\sqrt{5}$$