Solve frac{sqrt{2}}{2}Vfrac{5sqrt{2}V}{2}=9.8

$$\frac { \sqrt { 2 } } { 2 } V \frac { 5 \sqrt { 2 } V } { 2 } = 9.8$$

Solve for V

$$V = \frac{7 \sqrt{2}}{5} \approx 1.979898987$$

$$V = -\frac{7 \sqrt{2}}{5} \approx -1.979898987$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$\sqrt{2}V\times \frac{5\sqrt{2}V}{2}=19.6$$

Express \sqrt{2}\times \frac{5\sqrt{2}V}{2} as a single fraction.

$$\frac{\sqrt{2}\times 5\sqrt{2}V}{2}V=19.6$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2\times 5V}{2}V=19.6$$

Cancel out 2 and 2.

$$5VV=19.6$$

Multiply V and V to get V^{2}.

$$5V^{2}=19.6$$

Divide both sides by 5.

$$V^{2}=\frac{19.6}{5}$$

Expand \frac{19.6}{5} by multiplying both numerator and the denominator by 10.

$$V^{2}=\frac{196}{50}$$

Reduce the fraction \frac{196}{50} to lowest terms by extracting and canceling out 2.

$$V^{2}=\frac{98}{25}$$

Take the square root of both sides of the equation.

$$V=\frac{7\sqrt{2}}{5} V=-\frac{7\sqrt{2}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$\sqrt{2}V\times \frac{5\sqrt{2}V}{2}=19.6$$

Express \sqrt{2}\times \frac{5\sqrt{2}V}{2} as a single fraction.

$$\frac{\sqrt{2}\times 5\sqrt{2}V}{2}V=19.6$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2\times 5V}{2}V=19.6$$

Cancel out 2 and 2.

$$5VV=19.6$$

Multiply V and V to get V^{2}.

$$5V^{2}=19.6$$

Subtract 19.6 from both sides.

$$5V^{2}-19.6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -19.6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$V=\frac{0±\sqrt{0^{2}-4\times 5\left(-19.6\right)}}{2\times 5}$$

Square 0.

$$V=\frac{0±\sqrt{-4\times 5\left(-19.6\right)}}{2\times 5}$$

Multiply -4 times 5.

$$V=\frac{0±\sqrt{-20\left(-19.6\right)}}{2\times 5}$$

Multiply -20 times -19.6.

$$V=\frac{0±\sqrt{392}}{2\times 5}$$

Take the square root of 392.

$$V=\frac{0±14\sqrt{2}}{2\times 5}$$

Multiply 2 times 5.

$$V=\frac{0±14\sqrt{2}}{10}$$

Now solve the equation V=\frac{0±14\sqrt{2}}{10} when ± is plus.

$$V=\frac{7\sqrt{2}}{5}$$

Now solve the equation V=\frac{0±14\sqrt{2}}{10} when ± is minus.

$$V=-\frac{7\sqrt{2}}{5}$$

The equation is now solved.

$$V=\frac{7\sqrt{2}}{5} V=-\frac{7\sqrt{2}}{5}$$