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Simplifying v(4v + -24) = -6 Reorder the terms: v(-24 + 4v) = -6 (-24 * v + 4v * v) = -6 (-24v + 4v2) = -6 Solving -24v + 4v2 = -6 Solving for variable 'v'. Reorder the terms: 6 + -24v + 4v2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -24v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -12v + 2v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -12v + 2v2)' equal to zero and attempt to solve: Simplifying 3 + -12v + 2v2 = 0 Solving 3 + -12v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -6v + v2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -6v + -1.5 + v2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -6v + v2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -6v + v2 = 0 + -1.5 -6v + v2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -6v + v2 = -1.5 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = -1.5 + 9 Reorder the terms: 9 + -6v + v2 = -1.5 + 9 Combine like terms: -1.5 + 9 = 7.5 9 + -6v + v2 = 7.5 Factor a perfect square on the left side: (v + -3)(v + -3) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (v + -3) equal to 2.738612788 and -2.738612788.Subproblem 1
v + -3 = 2.738612788 Simplifying v + -3 = 2.738612788 Reorder the terms: -3 + v = 2.738612788 Solving -3 + v = 2.738612788 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 2.738612788 + 3 Combine like terms: -3 + 3 = 0 0 + v = 2.738612788 + 3 v = 2.738612788 + 3 Combine like terms: 2.738612788 + 3 = 5.738612788 v = 5.738612788 Simplifying v = 5.738612788Subproblem 2
v + -3 = -2.738612788 Simplifying v + -3 = -2.738612788 Reorder the terms: -3 + v = -2.738612788 Solving -3 + v = -2.738612788 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -2.738612788 + 3 Combine like terms: -3 + 3 = 0 0 + v = -2.738612788 + 3 v = -2.738612788 + 3 Combine like terms: -2.738612788 + 3 = 0.261387212 v = 0.261387212 Simplifying v = 0.261387212Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.738612788, 0.261387212}Solution
v = {5.738612788, 0.261387212}
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