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Simplifying 120 = 0.04v2 + 1.1v Reorder the terms: 120 = 1.1v + 0.04v2 Solving 120 = 1.1v + 0.04v2 Solving for variable 'v'. Reorder the terms: 120 + -1.1v + -0.04v2 = 1.1v + -1.1v + 0.04v2 + -0.04v2 Combine like terms: 1.1v + -1.1v = 0.0 120 + -1.1v + -0.04v2 = 0.0 + 0.04v2 + -0.04v2 120 + -1.1v + -0.04v2 = 0.04v2 + -0.04v2 Combine like terms: 0.04v2 + -0.04v2 = 0.00 120 + -1.1v + -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'. -3000 + 27.5v + v2 = 0 Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 27.5v + 3000 + v2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 27.5v + v2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 27.5v + v2 = 0 + 3000 27.5v + v2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 27.5v + v2 = 3000 The v term is 27.5v. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5v + 189.0625 + v2 = 3000 + 189.0625 Reorder the terms: 189.0625 + 27.5v + v2 = 3000 + 189.0625 Combine like terms: 3000 + 189.0625 = 3189.0625 189.0625 + 27.5v + v2 = 3189.0625 Factor a perfect square on the left side: (v + 13.75)(v + 13.75) = 3189.0625 Calculate the square root of the right side: 56.47178499 Break this problem into two subproblems by setting (v + 13.75) equal to 56.47178499 and -56.47178499.Subproblem 1
v + 13.75 = 56.47178499 Simplifying v + 13.75 = 56.47178499 Reorder the terms: 13.75 + v = 56.47178499 Solving 13.75 + v = 56.47178499 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + v = 56.47178499 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = 56.47178499 + -13.75 v = 56.47178499 + -13.75 Combine like terms: 56.47178499 + -13.75 = 42.72178499 v = 42.72178499 Simplifying v = 42.72178499Subproblem 2
v + 13.75 = -56.47178499 Simplifying v + 13.75 = -56.47178499 Reorder the terms: 13.75 + v = -56.47178499 Solving 13.75 + v = -56.47178499 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + v = -56.47178499 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = -56.47178499 + -13.75 v = -56.47178499 + -13.75 Combine like terms: -56.47178499 + -13.75 = -70.22178499 v = -70.22178499 Simplifying v = -70.22178499Solution
The solution to the problem is based on the solutions from the subproblems. v = {42.72178499, -70.22178499}
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