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Simplifying 250 = 0.04v2 + 1.1v Reorder the terms: 250 = 1.1v + 0.04v2 Solving 250 = 1.1v + 0.04v2 Solving for variable 'v'. Reorder the terms: 250 + -1.1v + -0.04v2 = 1.1v + -1.1v + 0.04v2 + -0.04v2 Combine like terms: 1.1v + -1.1v = 0.0 250 + -1.1v + -0.04v2 = 0.0 + 0.04v2 + -0.04v2 250 + -1.1v + -0.04v2 = 0.04v2 + -0.04v2 Combine like terms: 0.04v2 + -0.04v2 = 0.00 250 + -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'. -6250 + 27.5v + v2 = 0 Move the constant term to the right: Add '6250' to each side of the equation. -6250 + 27.5v + 6250 + v2 = 0 + 6250 Reorder the terms: -6250 + 6250 + 27.5v + v2 = 0 + 6250 Combine like terms: -6250 + 6250 = 0 0 + 27.5v + v2 = 0 + 6250 27.5v + v2 = 0 + 6250 Combine like terms: 0 + 6250 = 6250 27.5v + v2 = 6250 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 = 6250 + 189.0625 Reorder the terms: 189.0625 + 27.5v + v2 = 6250 + 189.0625 Combine like terms: 6250 + 189.0625 = 6439.0625 189.0625 + 27.5v + v2 = 6439.0625 Factor a perfect square on the left side: (v + 13.75)(v + 13.75) = 6439.0625 Calculate the square root of the right side: 80.243769229 Break this problem into two subproblems by setting (v + 13.75) equal to 80.243769229 and -80.243769229.Subproblem 1
v + 13.75 = 80.243769229 Simplifying v + 13.75 = 80.243769229 Reorder the terms: 13.75 + v = 80.243769229 Solving 13.75 + v = 80.243769229 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 = 80.243769229 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = 80.243769229 + -13.75 v = 80.243769229 + -13.75 Combine like terms: 80.243769229 + -13.75 = 66.493769229 v = 66.493769229 Simplifying v = 66.493769229Subproblem 2
v + 13.75 = -80.243769229 Simplifying v + 13.75 = -80.243769229 Reorder the terms: 13.75 + v = -80.243769229 Solving 13.75 + v = -80.243769229 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 = -80.243769229 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = -80.243769229 + -13.75 v = -80.243769229 + -13.75 Combine like terms: -80.243769229 + -13.75 = -93.993769229 v = -93.993769229 Simplifying v = -93.993769229Solution
The solution to the problem is based on the solutions from the subproblems. v = {66.493769229, -93.993769229}
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