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Simplifying 4v3(2v2 + -3v + 5) = 0 Reorder the terms: 4v3(5 + -3v + 2v2) = 0 (5 * 4v3 + -3v * 4v3 + 2v2 * 4v3) = 0 (20v3 + -12v4 + 8v5) = 0 Solving 20v3 + -12v4 + 8v5 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4v3'. 4v3(5 + -3v + 2v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'v3' equal to zero and attempt to solve: Simplifying v3 = 0 Solving v3 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + -3v + 2v2)' equal to zero and attempt to solve: Simplifying 5 + -3v + 2v2 = 0 Solving 5 + -3v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -1.5v + v2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1.5v + -2.5 + v2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1.5v + v2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1.5v + v2 = 0 + -2.5 -1.5v + v2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1.5v + v2 = -2.5 The v term is -1.5v. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5v + 0.5625 + v2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + -1.5v + v2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + -1.5v + v2 = -1.9375 Factor a perfect square on the left side: (v + -0.75)(v + -0.75) = -1.9375 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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