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Simplifying 4v3 + 36v2 + 10v = 0 Reorder the terms: 10v + 36v2 + 4v3 = 0 Solving 10v + 36v2 + 4v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2v'. 2v(5 + 18v + 2v2) = 0 Ignore the factor 2.Subproblem 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 '(5 + 18v + 2v2)' equal to zero and attempt to solve: Simplifying 5 + 18v + 2v2 = 0 Solving 5 + 18v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 9v + v2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 9v + -2.5 + v2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 9v + v2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 9v + v2 = 0 + -2.5 9v + v2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 9v + v2 = -2.5 The v term is 9v. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9v + 20.25 + v2 = -2.5 + 20.25 Reorder the terms: 20.25 + 9v + v2 = -2.5 + 20.25 Combine like terms: -2.5 + 20.25 = 17.75 20.25 + 9v + v2 = 17.75 Factor a perfect square on the left side: (v + 4.5)(v + 4.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (v + 4.5) equal to 4.213074887 and -4.213074887.Subproblem 1
v + 4.5 = 4.213074887 Simplifying v + 4.5 = 4.213074887 Reorder the terms: 4.5 + v = 4.213074887 Solving 4.5 + v = 4.213074887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = 4.213074887 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = 4.213074887 + -4.5 v = 4.213074887 + -4.5 Combine like terms: 4.213074887 + -4.5 = -0.286925113 v = -0.286925113 Simplifying v = -0.286925113Subproblem 2
v + 4.5 = -4.213074887 Simplifying v + 4.5 = -4.213074887 Reorder the terms: 4.5 + v = -4.213074887 Solving 4.5 + v = -4.213074887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = -4.213074887 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = -4.213074887 + -4.5 v = -4.213074887 + -4.5 Combine like terms: -4.213074887 + -4.5 = -8.713074887 v = -8.713074887 Simplifying v = -8.713074887Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.286925113, -8.713074887}Solution
v = {0, -0.286925113, -8.713074887}
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