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Simplifying 3v3 + 55v2 + -175v = 0 Reorder the terms: -175v + 55v2 + 3v3 = 0 Solving -175v + 55v2 + 3v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), 'v'. v(-175 + 55v + 3v2) = 0Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(-175 + 55v + 3v2)' equal to zero and attempt to solve: Simplifying -175 + 55v + 3v2 = 0 Solving -175 + 55v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -58.33333333 + 18.33333333v + v2 = 0 Move the constant term to the right: Add '58.33333333' to each side of the equation. -58.33333333 + 18.33333333v + 58.33333333 + v2 = 0 + 58.33333333 Reorder the terms: -58.33333333 + 58.33333333 + 18.33333333v + v2 = 0 + 58.33333333 Combine like terms: -58.33333333 + 58.33333333 = 0.00000000 0.00000000 + 18.33333333v + v2 = 0 + 58.33333333 18.33333333v + v2 = 0 + 58.33333333 Combine like terms: 0 + 58.33333333 = 58.33333333 18.33333333v + v2 = 58.33333333 The v term is 18.33333333v. Take half its coefficient (9.166666665). Square it (84.02777775) and add it to both sides. Add '84.02777775' to each side of the equation. 18.33333333v + 84.02777775 + v2 = 58.33333333 + 84.02777775 Reorder the terms: 84.02777775 + 18.33333333v + v2 = 58.33333333 + 84.02777775 Combine like terms: 58.33333333 + 84.02777775 = 142.36111108 84.02777775 + 18.33333333v + v2 = 142.36111108 Factor a perfect square on the left side: (v + 9.166666665)(v + 9.166666665) = 142.36111108 Calculate the square root of the right side: 11.931517551 Break this problem into two subproblems by setting (v + 9.166666665) equal to 11.931517551 and -11.931517551.Subproblem 1
v + 9.166666665 = 11.931517551 Simplifying v + 9.166666665 = 11.931517551 Reorder the terms: 9.166666665 + v = 11.931517551 Solving 9.166666665 + v = 11.931517551 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + v = 11.931517551 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + v = 11.931517551 + -9.166666665 v = 11.931517551 + -9.166666665 Combine like terms: 11.931517551 + -9.166666665 = 2.764850886 v = 2.764850886 Simplifying v = 2.764850886Subproblem 2
v + 9.166666665 = -11.931517551 Simplifying v + 9.166666665 = -11.931517551 Reorder the terms: 9.166666665 + v = -11.931517551 Solving 9.166666665 + v = -11.931517551 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + v = -11.931517551 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + v = -11.931517551 + -9.166666665 v = -11.931517551 + -9.166666665 Combine like terms: -11.931517551 + -9.166666665 = -21.098184216 v = -21.098184216 Simplifying v = -21.098184216Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.764850886, -21.098184216}Solution
v = {0, 2.764850886, -21.098184216}
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