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Simplifying 6(6v + 6) + -6v(v + -7) = 0 Reorder the terms: 6(6 + 6v) + -6v(v + -7) = 0 (6 * 6 + 6v * 6) + -6v(v + -7) = 0 (36 + 36v) + -6v(v + -7) = 0 Reorder the terms: 36 + 36v + -6v(-7 + v) = 0 36 + 36v + (-7 * -6v + v * -6v) = 0 36 + 36v + (42v + -6v2) = 0 Combine like terms: 36v + 42v = 78v 36 + 78v + -6v2 = 0 Solving 36 + 78v + -6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6'. 6(6 + 13v + -1v2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(6 + 13v + -1v2)' equal to zero and attempt to solve: Simplifying 6 + 13v + -1v2 = 0 Solving 6 + 13v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -13v + v2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -13v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + -13v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -13v + v2 = 0 + 6 -13v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 -13v + v2 = 6 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 = 6 + 42.25 Reorder the terms: 42.25 + -13v + v2 = 6 + 42.25 Combine like terms: 6 + 42.25 = 48.25 42.25 + -13v + v2 = 48.25 Factor a perfect square on the left side: (v + -6.5)(v + -6.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (v + -6.5) equal to 6.946221995 and -6.946221995.Subproblem 1
v + -6.5 = 6.946221995 Simplifying v + -6.5 = 6.946221995 Reorder the terms: -6.5 + v = 6.946221995 Solving -6.5 + v = 6.946221995 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 = 6.946221995 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + v = 6.946221995 + 6.5 v = 6.946221995 + 6.5 Combine like terms: 6.946221995 + 6.5 = 13.446221995 v = 13.446221995 Simplifying v = 13.446221995Subproblem 2
v + -6.5 = -6.946221995 Simplifying v + -6.5 = -6.946221995 Reorder the terms: -6.5 + v = -6.946221995 Solving -6.5 + v = -6.946221995 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 = -6.946221995 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + v = -6.946221995 + 6.5 v = -6.946221995 + 6.5 Combine like terms: -6.946221995 + 6.5 = -0.446221995 v = -0.446221995 Simplifying v = -0.446221995Solution
The solution to the problem is based on the solutions from the subproblems. v = {13.446221995, -0.446221995}Solution
v = {13.446221995, -0.446221995}
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