Rewrite the equation as .

Multiply by .

Multiply by .

Multiply .

Combine and .

Combine and .

Factor out of .

Factor out of .

Separate fractions.

Divide by .

Divide by .

Simplify the expression.

Raise to the power of .

Multiply by .

Combine and .

Divide by .

Subtract from both sides of the equation.

Subtract from .

Divide each term in by .

Cancel the common factor of .

Divide by .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for v 1/2*((0.12)(7.85^2))=(0.12)(9.81)(1.18)+1/2*((0.12)v^2)