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Simplifying -2v(5v + -4) + 9v = 5(v + 2) Reorder the terms: -2v(-4 + 5v) + 9v = 5(v + 2) (-4 * -2v + 5v * -2v) + 9v = 5(v + 2) (8v + -10v2) + 9v = 5(v + 2) Reorder the terms: 8v + 9v + -10v2 = 5(v + 2) Combine like terms: 8v + 9v = 17v 17v + -10v2 = 5(v + 2) Reorder the terms: 17v + -10v2 = 5(2 + v) 17v + -10v2 = (2 * 5 + v * 5) 17v + -10v2 = (10 + 5v) Solving 17v + -10v2 = 10 + 5v Solving for variable 'v'. Reorder the terms: -10 + 17v + -5v + -10v2 = 10 + 5v + -10 + -5v Combine like terms: 17v + -5v = 12v -10 + 12v + -10v2 = 10 + 5v + -10 + -5v Reorder the terms: -10 + 12v + -10v2 = 10 + -10 + 5v + -5v Combine like terms: 10 + -10 = 0 -10 + 12v + -10v2 = 0 + 5v + -5v -10 + 12v + -10v2 = 5v + -5v Combine like terms: 5v + -5v = 0 -10 + 12v + -10v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 6v + -5v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 6v + -5v2)' equal to zero and attempt to solve: Simplifying -5 + 6v + -5v2 = 0 Solving -5 + 6v + -5v2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1 + -1.2v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.2v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + -1.2v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.2v + v2 = 0 + -1 -1.2v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.2v + v2 = -1 The v term is -1.2v. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2v + 0.36 + v2 = -1 + 0.36 Reorder the terms: 0.36 + -1.2v + v2 = -1 + 0.36 Combine like terms: -1 + 0.36 = -0.64 0.36 + -1.2v + v2 = -0.64 Factor a perfect square on the left side: (v + -0.6)(v + -0.6) = -0.64 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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