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Simplifying 3v6 + 15v5 + 42v4 = 0 Reorder the terms: 42v4 + 15v5 + 3v6 = 0 Solving 42v4 + 15v5 + 3v6 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3v4'. 3v4(14 + 5v + v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'v4' equal to zero and attempt to solve: Simplifying v4 = 0 Solving v4 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v4 = 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 '(14 + 5v + v2)' equal to zero and attempt to solve: Simplifying 14 + 5v + v2 = 0 Solving 14 + 5v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 5v + -14 + v2 = 0 + -14 Reorder the terms: 14 + -14 + 5v + v2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 5v + v2 = 0 + -14 5v + v2 = 0 + -14 Combine like terms: 0 + -14 = -14 5v + v2 = -14 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 = -14 + 6.25 Reorder the terms: 6.25 + 5v + v2 = -14 + 6.25 Combine like terms: -14 + 6.25 = -7.75 6.25 + 5v + v2 = -7.75 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = -7.75 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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