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Simplifying 4v3 + 20v2 + 36v = 0 Reorder the terms: 36v + 20v2 + 4v3 = 0 Solving 36v + 20v2 + 4v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4v'. 4v(9 + 5v + v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(9 + 5v + v2)' equal to zero and attempt to solve: Simplifying 9 + 5v + v2 = 0 Solving 9 + 5v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 5v + -9 + v2 = 0 + -9 Reorder the terms: 9 + -9 + 5v + v2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5v + v2 = 0 + -9 5v + v2 = 0 + -9 Combine like terms: 0 + -9 = -9 5v + v2 = -9 The v term is 5v. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5v + 6.25 + v2 = -9 + 6.25 Reorder the terms: 6.25 + 5v + v2 = -9 + 6.25 Combine like terms: -9 + 6.25 = -2.75 6.25 + 5v + v2 = -2.75 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = -2.75 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.Solution
v = {0}
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