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Simplifying 6v2 + 12v + 89 = 8 Reorder the terms: 89 + 12v + 6v2 = 8 Solving 89 + 12v + 6v2 = 8 Solving for variable 'v'. Reorder the terms: 89 + -8 + 12v + 6v2 = 8 + -8 Combine like terms: 89 + -8 = 81 81 + 12v + 6v2 = 8 + -8 Combine like terms: 8 + -8 = 0 81 + 12v + 6v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(27 + 4v + 2v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(27 + 4v + 2v2)' equal to zero and attempt to solve: Simplifying 27 + 4v + 2v2 = 0 Solving 27 + 4v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + 2v + v2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 2v + -13.5 + v2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 2v + v2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 2v + v2 = 0 + -13.5 2v + v2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 2v + v2 = -13.5 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = -13.5 + 1 Reorder the terms: 1 + 2v + v2 = -13.5 + 1 Combine like terms: -13.5 + 1 = -12.5 1 + 2v + v2 = -12.5 Factor a perfect square on the left side: (v + 1)(v + 1) = -12.5 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. The solution to this equation could not be determined.
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