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Simplifying 12v2 + 12v + -15 = 0 Reorder the terms: -15 + 12v + 12v2 = 0 Solving -15 + 12v + 12v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 4v + 4v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 4v + 4v2)' equal to zero and attempt to solve: Simplifying -5 + 4v + 4v2 = 0 Solving -5 + 4v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + v + v2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + v + 1.25 + v2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + v + v2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + v + v2 = 0 + 1.25 v + v2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 v + v2 = 1.25 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + v2 = 1.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 1.25 + 0.25 Combine like terms: 1.25 + 0.25 = 1.5 1.25 + v2 = 1.5 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (v + 0.5) equal to 1.224744871 and -1.224744871.Subproblem 1
v + 0.5 = 1.224744871 Simplifying v + 0.5 = 1.224744871 Reorder the terms: 0.5 + v = 1.224744871 Solving 0.5 + v = 1.224744871 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 1.224744871 + -0.5 v = 1.224744871 + -0.5 Combine like terms: 1.224744871 + -0.5 = 0.724744871 v = 0.724744871 Simplifying v = 0.724744871Subproblem 2
v + 0.5 = -1.224744871 Simplifying v + 0.5 = -1.224744871 Reorder the terms: 0.5 + v = -1.224744871 Solving 0.5 + v = -1.224744871 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -1.224744871 + -0.5 v = -1.224744871 + -0.5 Combine like terms: -1.224744871 + -0.5 = -1.724744871 v = -1.724744871 Simplifying v = -1.724744871Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.724744871, -1.724744871}Solution
v = {0.724744871, -1.724744871}
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