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Simplifying 6v3 + 6v2 + 168v = 0 Reorder the terms: 168v + 6v2 + 6v3 = 0 Solving 168v + 6v2 + 6v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6v'. 6v(28 + v + v2) = 0 Ignore the factor 6.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 '(28 + v + v2)' equal to zero and attempt to solve: Simplifying 28 + v + v2 = 0 Solving 28 + v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + v + -28 + v2 = 0 + -28 Reorder the terms: 28 + -28 + v + v2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + v + v2 = 0 + -28 v + v2 = 0 + -28 Combine like terms: 0 + -28 = -28 v + v2 = -28 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. v + 0.25 + v2 = -28 + 0.25 Reorder the terms: 0.25 + v + v2 = -28 + 0.25 Combine like terms: -28 + 0.25 = -27.75 0.25 + v + v2 = -27.75 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = -27.75 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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