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Simplifying 6v2 + -78v + -252 = 0 Reorder the terms: -252 + -78v + 6v2 = 0 Solving -252 + -78v + 6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6'. 6(-42 + -13v + v2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-42 + -13v + v2)' equal to zero and attempt to solve: Simplifying -42 + -13v + v2 = 0 Solving -42 + -13v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -13v + 42 + v2 = 0 + 42 Reorder the terms: -42 + 42 + -13v + v2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -13v + v2 = 0 + 42 -13v + v2 = 0 + 42 Combine like terms: 0 + 42 = 42 -13v + v2 = 42 The v term is -13v. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13v + 42.25 + v2 = 42 + 42.25 Reorder the terms: 42.25 + -13v + v2 = 42 + 42.25 Combine like terms: 42 + 42.25 = 84.25 42.25 + -13v + v2 = 84.25 Factor a perfect square on the left side: (v + -6.5)(v + -6.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (v + -6.5) equal to 9.178779875 and -9.178779875.Subproblem 1
v + -6.5 = 9.178779875 Simplifying v + -6.5 = 9.178779875 Reorder the terms: -6.5 + v = 9.178779875 Solving -6.5 + v = 9.178779875 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + v = 9.178779875 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + v = 9.178779875 + 6.5 v = 9.178779875 + 6.5 Combine like terms: 9.178779875 + 6.5 = 15.678779875 v = 15.678779875 Simplifying v = 15.678779875Subproblem 2
v + -6.5 = -9.178779875 Simplifying v + -6.5 = -9.178779875 Reorder the terms: -6.5 + v = -9.178779875 Solving -6.5 + v = -9.178779875 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + v = -9.178779875 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + v = -9.178779875 + 6.5 v = -9.178779875 + 6.5 Combine like terms: -9.178779875 + 6.5 = -2.678779875 v = -2.678779875 Simplifying v = -2.678779875Solution
The solution to the problem is based on the solutions from the subproblems. v = {15.678779875, -2.678779875}Solution
v = {15.678779875, -2.678779875}
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