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Simplifying -2v + -1v + 12 = -3v2 + 6v Reorder the terms: 12 + -2v + -1v = -3v2 + 6v Combine like terms: -2v + -1v = -3v 12 + -3v = -3v2 + 6v Reorder the terms: 12 + -3v = 6v + -3v2 Solving 12 + -3v = 6v + -3v2 Solving for variable 'v'. Combine like terms: -3v + -6v = -9v 12 + -9v + 3v2 = 6v + -3v2 + -6v + 3v2 Reorder the terms: 12 + -9v + 3v2 = 6v + -6v + -3v2 + 3v2 Combine like terms: 6v + -6v = 0 12 + -9v + 3v2 = 0 + -3v2 + 3v2 12 + -9v + 3v2 = -3v2 + 3v2 Combine like terms: -3v2 + 3v2 = 0 12 + -9v + 3v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -3v + v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -3v + v2)' equal to zero and attempt to solve: Simplifying 4 + -3v + v2 = 0 Solving 4 + -3v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3v + -4 + v2 = 0 + -4 Reorder the terms: 4 + -4 + -3v + v2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3v + v2 = 0 + -4 -3v + v2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3v + v2 = -4 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 = -4 + 2.25 Reorder the terms: 2.25 + -3v + v2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3v + v2 = -1.75 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = -1.75 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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