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Simplifying 72 = 0.04v2 + 1.1v Reorder the terms: 72 = 1.1v + 0.04v2 Solving 72 = 1.1v + 0.04v2 Solving for variable 'v'. Reorder the terms: 72 + -1.1v + -0.04v2 = 1.1v + -1.1v + 0.04v2 + -0.04v2 Combine like terms: 1.1v + -1.1v = 0.0 72 + -1.1v + -0.04v2 = 0.0 + 0.04v2 + -0.04v2 72 + -1.1v + -0.04v2 = 0.04v2 + -0.04v2 Combine like terms: 0.04v2 + -0.04v2 = 0.00 72 + -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'. -1800 + 27.5v + v2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + 27.5v + 1800 + v2 = 0 + 1800 Reorder the terms: -1800 + 1800 + 27.5v + v2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + 27.5v + v2 = 0 + 1800 27.5v + v2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 27.5v + v2 = 1800 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 = 1800 + 189.0625 Reorder the terms: 189.0625 + 27.5v + v2 = 1800 + 189.0625 Combine like terms: 1800 + 189.0625 = 1989.0625 189.0625 + 27.5v + v2 = 1989.0625 Factor a perfect square on the left side: (v + 13.75)(v + 13.75) = 1989.0625 Calculate the square root of the right side: 44.598906937 Break this problem into two subproblems by setting (v + 13.75) equal to 44.598906937 and -44.598906937.Subproblem 1
v + 13.75 = 44.598906937 Simplifying v + 13.75 = 44.598906937 Reorder the terms: 13.75 + v = 44.598906937 Solving 13.75 + v = 44.598906937 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 = 44.598906937 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = 44.598906937 + -13.75 v = 44.598906937 + -13.75 Combine like terms: 44.598906937 + -13.75 = 30.848906937 v = 30.848906937 Simplifying v = 30.848906937Subproblem 2
v + 13.75 = -44.598906937 Simplifying v + 13.75 = -44.598906937 Reorder the terms: 13.75 + v = -44.598906937 Solving 13.75 + v = -44.598906937 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 = -44.598906937 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = -44.598906937 + -13.75 v = -44.598906937 + -13.75 Combine like terms: -44.598906937 + -13.75 = -58.348906937 v = -58.348906937 Simplifying v = -58.348906937Solution
The solution to the problem is based on the solutions from the subproblems. v = {30.848906937, -58.348906937}
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