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Simplifying -3v2 + 60v + -81 = 0 Reorder the terms: -81 + 60v + -3v2 = 0 Solving -81 + 60v + -3v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + 20v + -1v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + 20v + -1v2)' equal to zero and attempt to solve: Simplifying -27 + 20v + -1v2 = 0 Solving -27 + 20v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -20v + v2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -20v + -27 + v2 = 0 + -27 Reorder the terms: 27 + -27 + -20v + v2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -20v + v2 = 0 + -27 -20v + v2 = 0 + -27 Combine like terms: 0 + -27 = -27 -20v + v2 = -27 The v term is -20v. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20v + 100 + v2 = -27 + 100 Reorder the terms: 100 + -20v + v2 = -27 + 100 Combine like terms: -27 + 100 = 73 100 + -20v + v2 = 73 Factor a perfect square on the left side: (v + -10)(v + -10) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (v + -10) equal to 8.544003745 and -8.544003745.Subproblem 1
v + -10 = 8.544003745 Simplifying v + -10 = 8.544003745 Reorder the terms: -10 + v = 8.544003745 Solving -10 + v = 8.544003745 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + v = 8.544003745 + 10 Combine like terms: -10 + 10 = 0 0 + v = 8.544003745 + 10 v = 8.544003745 + 10 Combine like terms: 8.544003745 + 10 = 18.544003745 v = 18.544003745 Simplifying v = 18.544003745Subproblem 2
v + -10 = -8.544003745 Simplifying v + -10 = -8.544003745 Reorder the terms: -10 + v = -8.544003745 Solving -10 + v = -8.544003745 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + v = -8.544003745 + 10 Combine like terms: -10 + 10 = 0 0 + v = -8.544003745 + 10 v = -8.544003745 + 10 Combine like terms: -8.544003745 + 10 = 1.455996255 v = 1.455996255 Simplifying v = 1.455996255Solution
The solution to the problem is based on the solutions from the subproblems. v = {18.544003745, 1.455996255}Solution
v = {18.544003745, 1.455996255}
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