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Simplifying 4 + -5v + -12v + -6v2 + -4 + -2v3 = 0 Reorder the terms: 4 + -4 + -5v + -12v + -6v2 + -2v3 = 0 Combine like terms: 4 + -4 = 0 0 + -5v + -12v + -6v2 + -2v3 = 0 -5v + -12v + -6v2 + -2v3 = 0 Combine like terms: -5v + -12v = -17v -17v + -6v2 + -2v3 = 0 Solving -17v + -6v2 + -2v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '-1v'. -1v(17 + 6v + 2v2) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(17 + 6v + 2v2)' equal to zero and attempt to solve: Simplifying 17 + 6v + 2v2 = 0 Solving 17 + 6v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 3v + v2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 3v + -8.5 + v2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 3v + v2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 3v + v2 = 0 + -8.5 3v + v2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 3v + v2 = -8.5 The v term is 3v. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3v + 2.25 + v2 = -8.5 + 2.25 Reorder the terms: 2.25 + 3v + v2 = -8.5 + 2.25 Combine like terms: -8.5 + 2.25 = -6.25 2.25 + 3v + v2 = -6.25 Factor a perfect square on the left side: (v + 1.5)(v + 1.5) = -6.25 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
v = {0}
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