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Simplifying 6v2 + 45v + -36 = 0 Reorder the terms: -36 + 45v + 6v2 = 0 Solving -36 + 45v + 6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 15v + 2v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + 15v + 2v2)' equal to zero and attempt to solve: Simplifying -12 + 15v + 2v2 = 0 Solving -12 + 15v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 7.5v + v2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 7.5v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + 7.5v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7.5v + v2 = 0 + 6 7.5v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 7.5v + v2 = 6 The v term is 7.5v. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5v + 14.0625 + v2 = 6 + 14.0625 Reorder the terms: 14.0625 + 7.5v + v2 = 6 + 14.0625 Combine like terms: 6 + 14.0625 = 20.0625 14.0625 + 7.5v + v2 = 20.0625 Factor a perfect square on the left side: (v + 3.75)(v + 3.75) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (v + 3.75) equal to 4.479118217 and -4.479118217.Subproblem 1
v + 3.75 = 4.479118217 Simplifying v + 3.75 = 4.479118217 Reorder the terms: 3.75 + v = 4.479118217 Solving 3.75 + v = 4.479118217 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + v = 4.479118217 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + v = 4.479118217 + -3.75 v = 4.479118217 + -3.75 Combine like terms: 4.479118217 + -3.75 = 0.729118217 v = 0.729118217 Simplifying v = 0.729118217Subproblem 2
v + 3.75 = -4.479118217 Simplifying v + 3.75 = -4.479118217 Reorder the terms: 3.75 + v = -4.479118217 Solving 3.75 + v = -4.479118217 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + v = -4.479118217 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + v = -4.479118217 + -3.75 v = -4.479118217 + -3.75 Combine like terms: -4.479118217 + -3.75 = -8.229118217 v = -8.229118217 Simplifying v = -8.229118217Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.729118217, -8.229118217}Solution
v = {0.729118217, -8.229118217}
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