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Simplifying 12v2 + -12v = 20 Reorder the terms: -12v + 12v2 = 20 Solving -12v + 12v2 = 20 Solving for variable 'v'. Reorder the terms: -20 + -12v + 12v2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -12v + 12v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -3v + 3v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -3v + 3v2)' equal to zero and attempt to solve: Simplifying -5 + -3v + 3v2 = 0 Solving -5 + -3v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + -1v + v2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1v + 1.666666667 + v2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1v + v2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1v + v2 = 0 + 1.666666667 -1v + v2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1v + v2 = 1.666666667 The v term is -1v. 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. -1v + 0.25 + v2 = 1.666666667 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 1.666666667 + 0.25 Combine like terms: 1.666666667 + 0.25 = 1.916666667 0.25 + -1v + v2 = 1.916666667 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 1.916666667 Calculate the square root of the right side: 1.384437311 Break this problem into two subproblems by setting (v + -0.5) equal to 1.384437311 and -1.384437311.Subproblem 1
v + -0.5 = 1.384437311 Simplifying v + -0.5 = 1.384437311 Reorder the terms: -0.5 + v = 1.384437311 Solving -0.5 + v = 1.384437311 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 = 1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 1.384437311 + 0.5 v = 1.384437311 + 0.5 Combine like terms: 1.384437311 + 0.5 = 1.884437311 v = 1.884437311 Simplifying v = 1.884437311Subproblem 2
v + -0.5 = -1.384437311 Simplifying v + -0.5 = -1.384437311 Reorder the terms: -0.5 + v = -1.384437311 Solving -0.5 + v = -1.384437311 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 = -1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -1.384437311 + 0.5 v = -1.384437311 + 0.5 Combine like terms: -1.384437311 + 0.5 = -0.884437311 v = -0.884437311 Simplifying v = -0.884437311Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.884437311, -0.884437311}Solution
v = {1.884437311, -0.884437311}
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