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Simplifying 2v4 + 2v3 + 2v2 = 0 Reorder the terms: 2v2 + 2v3 + 2v4 = 0 Solving 2v2 + 2v3 + 2v4 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2v2'. 2v2(1 + v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve: Simplifying v2 = 0 Solving v2 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v2 = 0 Take the square root of each side: v = {0}Subproblem 2
Set the factor '(1 + v + v2)' equal to zero and attempt to solve: Simplifying 1 + v + v2 = 0 Solving 1 + v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + v + v2 = 0 + -1 v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 v + v2 = -1 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 = -1 + 0.25 Reorder the terms: 0.25 + v + v2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + v + v2 = -0.75 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = -0.75 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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