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Simplifying 0 = -6v2 + -15v + -12 Reorder the terms: 0 = -12 + -15v + -6v2 Solving 0 = -12 + -15v + -6v2 Solving for variable 'v'. Combine like terms: 0 + 12 = 12 12 + 15v + 6v2 = -12 + -15v + -6v2 + 12 + 15v + 6v2 Reorder the terms: 12 + 15v + 6v2 = -12 + 12 + -15v + 15v + -6v2 + 6v2 Combine like terms: -12 + 12 = 0 12 + 15v + 6v2 = 0 + -15v + 15v + -6v2 + 6v2 12 + 15v + 6v2 = -15v + 15v + -6v2 + 6v2 Combine like terms: -15v + 15v = 0 12 + 15v + 6v2 = 0 + -6v2 + 6v2 12 + 15v + 6v2 = -6v2 + 6v2 Combine like terms: -6v2 + 6v2 = 0 12 + 15v + 6v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 5v + 2v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 5v + 2v2)' equal to zero and attempt to solve: Simplifying 4 + 5v + 2v2 = 0 Solving 4 + 5v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 2.5v + v2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2.5v + -2 + v2 = 0 + -2 Reorder the terms: 2 + -2 + 2.5v + v2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2.5v + v2 = 0 + -2 2.5v + v2 = 0 + -2 Combine like terms: 0 + -2 = -2 2.5v + v2 = -2 The v term is 2.5v. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5v + 1.5625 + v2 = -2 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = -2 + 1.5625 Combine like terms: -2 + 1.5625 = -0.4375 1.5625 + 2.5v + v2 = -0.4375 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = -0.4375 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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