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Simplifying 0.02v2 + 1.4v + -480 = 0 Reorder the terms: -480 + 1.4v + 0.02v2 = 0 Solving -480 + 1.4v + 0.02v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -24000 + 70v + v2 = 0 Move the constant term to the right: Add '24000' to each side of the equation. -24000 + 70v + 24000 + v2 = 0 + 24000 Reorder the terms: -24000 + 24000 + 70v + v2 = 0 + 24000 Combine like terms: -24000 + 24000 = 0 0 + 70v + v2 = 0 + 24000 70v + v2 = 0 + 24000 Combine like terms: 0 + 24000 = 24000 70v + v2 = 24000 The v term is 70v. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70v + 1225 + v2 = 24000 + 1225 Reorder the terms: 1225 + 70v + v2 = 24000 + 1225 Combine like terms: 24000 + 1225 = 25225 1225 + 70v + v2 = 25225 Factor a perfect square on the left side: (v + 35)(v + 35) = 25225 Calculate the square root of the right side: 158.823801743 Break this problem into two subproblems by setting (v + 35) equal to 158.823801743 and -158.823801743.Subproblem 1
v + 35 = 158.823801743 Simplifying v + 35 = 158.823801743 Reorder the terms: 35 + v = 158.823801743 Solving 35 + v = 158.823801743 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + v = 158.823801743 + -35 Combine like terms: 35 + -35 = 0 0 + v = 158.823801743 + -35 v = 158.823801743 + -35 Combine like terms: 158.823801743 + -35 = 123.823801743 v = 123.823801743 Simplifying v = 123.823801743Subproblem 2
v + 35 = -158.823801743 Simplifying v + 35 = -158.823801743 Reorder the terms: 35 + v = -158.823801743 Solving 35 + v = -158.823801743 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + v = -158.823801743 + -35 Combine like terms: 35 + -35 = 0 0 + v = -158.823801743 + -35 v = -158.823801743 + -35 Combine like terms: -158.823801743 + -35 = -193.823801743 v = -193.823801743 Simplifying v = -193.823801743Solution
The solution to the problem is based on the solutions from the subproblems. v = {123.823801743, -193.823801743}
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