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Simplifying 2v2 + -17v + 34 = v + -4v2 Reorder the terms: 34 + -17v + 2v2 = v + -4v2 Solving 34 + -17v + 2v2 = v + -4v2 Solving for variable 'v'. Reorder the terms: 34 + -17v + -1v + 2v2 + 4v2 = v + -4v2 + -1v + 4v2 Combine like terms: -17v + -1v = -18v 34 + -18v + 2v2 + 4v2 = v + -4v2 + -1v + 4v2 Combine like terms: 2v2 + 4v2 = 6v2 34 + -18v + 6v2 = v + -4v2 + -1v + 4v2 Reorder the terms: 34 + -18v + 6v2 = v + -1v + -4v2 + 4v2 Combine like terms: v + -1v = 0 34 + -18v + 6v2 = 0 + -4v2 + 4v2 34 + -18v + 6v2 = -4v2 + 4v2 Combine like terms: -4v2 + 4v2 = 0 34 + -18v + 6v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -9v + 3v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -9v + 3v2)' equal to zero and attempt to solve: Simplifying 17 + -9v + 3v2 = 0 Solving 17 + -9v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.666666667 + -3v + v2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + -3v + -5.666666667 + v2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + -3v + v2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + -3v + v2 = 0 + -5.666666667 -3v + v2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 -3v + v2 = -5.666666667 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 = -5.666666667 + 2.25 Reorder the terms: 2.25 + -3v + v2 = -5.666666667 + 2.25 Combine like terms: -5.666666667 + 2.25 = -3.416666667 2.25 + -3v + v2 = -3.416666667 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = -3.416666667 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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