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Simplifying 3v4 + -18v3 + 51v2 = 0 Reorder the terms: 51v2 + -18v3 + 3v4 = 0 Solving 51v2 + -18v3 + 3v4 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3v2'. 3v2(17 + -6v + v2) = 0 Ignore the factor 3.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 '(17 + -6v + v2)' equal to zero and attempt to solve: Simplifying 17 + -6v + v2 = 0 Solving 17 + -6v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -6v + -17 + v2 = 0 + -17 Reorder the terms: 17 + -17 + -6v + v2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -6v + v2 = 0 + -17 -6v + v2 = 0 + -17 Combine like terms: 0 + -17 = -17 -6v + v2 = -17 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = -17 + 9 Reorder the terms: 9 + -6v + v2 = -17 + 9 Combine like terms: -17 + 9 = -8 9 + -6v + v2 = -8 Factor a perfect square on the left side: (v + -3)(v + -3) = -8 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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