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Simplifying 0 = 0.04v2 + 1.2v + -150 Reorder the terms: 0 = -150 + 1.2v + 0.04v2 Solving 0 = -150 + 1.2v + 0.04v2 Solving for variable 'v'. Combine like terms: 0 + 150 = 150 150 + -1.2v + -0.04v2 = -150 + 1.2v + 0.04v2 + 150 + -1.2v + -0.04v2 Reorder the terms: 150 + -1.2v + -0.04v2 = -150 + 150 + 1.2v + -1.2v + 0.04v2 + -0.04v2 Combine like terms: -150 + 150 = 0 150 + -1.2v + -0.04v2 = 0 + 1.2v + -1.2v + 0.04v2 + -0.04v2 150 + -1.2v + -0.04v2 = 1.2v + -1.2v + 0.04v2 + -0.04v2 Combine like terms: 1.2v + -1.2v = 0.0 150 + -1.2v + -0.04v2 = 0.0 + 0.04v2 + -0.04v2 150 + -1.2v + -0.04v2 = 0.04v2 + -0.04v2 Combine like terms: 0.04v2 + -0.04v2 = 0.00 150 + -1.2v + -0.04v2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -3750 + 30v + v2 = 0 Move the constant term to the right: Add '3750' to each side of the equation. -3750 + 30v + 3750 + v2 = 0 + 3750 Reorder the terms: -3750 + 3750 + 30v + v2 = 0 + 3750 Combine like terms: -3750 + 3750 = 0 0 + 30v + v2 = 0 + 3750 30v + v2 = 0 + 3750 Combine like terms: 0 + 3750 = 3750 30v + v2 = 3750 The v term is 30v. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30v + 225 + v2 = 3750 + 225 Reorder the terms: 225 + 30v + v2 = 3750 + 225 Combine like terms: 3750 + 225 = 3975 225 + 30v + v2 = 3975 Factor a perfect square on the left side: (v + 15)(v + 15) = 3975 Calculate the square root of the right side: 63.047601065 Break this problem into two subproblems by setting (v + 15) equal to 63.047601065 and -63.047601065.Subproblem 1
v + 15 = 63.047601065 Simplifying v + 15 = 63.047601065 Reorder the terms: 15 + v = 63.047601065 Solving 15 + v = 63.047601065 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + v = 63.047601065 + -15 Combine like terms: 15 + -15 = 0 0 + v = 63.047601065 + -15 v = 63.047601065 + -15 Combine like terms: 63.047601065 + -15 = 48.047601065 v = 48.047601065 Simplifying v = 48.047601065Subproblem 2
v + 15 = -63.047601065 Simplifying v + 15 = -63.047601065 Reorder the terms: 15 + v = -63.047601065 Solving 15 + v = -63.047601065 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + v = -63.047601065 + -15 Combine like terms: 15 + -15 = 0 0 + v = -63.047601065 + -15 v = -63.047601065 + -15 Combine like terms: -63.047601065 + -15 = -78.047601065 v = -78.047601065 Simplifying v = -78.047601065Solution
The solution to the problem is based on the solutions from the subproblems. v = {48.047601065, -78.047601065}
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