Solve 80=0.05v^2

$$80 = 0.05 v ^ { 2 }$$

Solve for v

$$v=40$$

$$v=-40$$

Steps Using Difference of Squares

Divide both sides by 0.05.

$$\frac{80}{0.05}=v^{2}$$

Expand \frac{80}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{8000}{5}=v^{2}$$

Divide 8000 by 5 to get 1600.

$$1600=v^{2}$$

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

$$v^{2}=1600$$

Subtract 1600 from both sides.

$$v^{2}-1600=0$$

Consider v^{2}-1600. Rewrite v^{2}-1600 as v^{2}-40^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-40\right)\left(v+40\right)=0$$

To find equation solutions, solve v-40=0 and v+40=0.

$$v=40 v=-40$$

Steps by Finding Square Root

Divide both sides by 0.05.

$$\frac{80}{0.05}=v^{2}$$

Expand \frac{80}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{8000}{5}=v^{2}$$

Divide 8000 by 5 to get 1600.

$$1600=v^{2}$$

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

$$v^{2}=1600$$

Take the square root of both sides of the equation.

$$v=40 v=-40$$

Steps Using the Quadratic Formula

Divide both sides by 0.05.

$$\frac{80}{0.05}=v^{2}$$

Expand \frac{80}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{8000}{5}=v^{2}$$

Divide 8000 by 5 to get 1600.

$$1600=v^{2}$$

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

$$v^{2}=1600$$

Subtract 1600 from both sides.

$$v^{2}-1600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-1600\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-1600\right)}}{2}$$

Multiply -4 times -1600.

$$v=\frac{0±\sqrt{6400}}{2}$$

Take the square root of 6400.

$$v=\frac{0±80}{2}$$

Now solve the equation v=\frac{0±80}{2} when ± is plus. Divide 80 by 2.

$$v=40$$

Now solve the equation v=\frac{0±80}{2} when ± is minus. Divide -80 by 2.

$$v=-40$$

The equation is now solved.

$$v=40 v=-40$$