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Simplifying -32v3 + 17v2 + 18v = 17v2 Reorder the terms: 18v + 17v2 + -32v3 = 17v2 Add '-17v2' to each side of the equation. 18v + 17v2 + -17v2 + -32v3 = 17v2 + -17v2 Combine like terms: 17v2 + -17v2 = 0 18v + 0 + -32v3 = 17v2 + -17v2 18v + -32v3 = 17v2 + -17v2 Combine like terms: 17v2 + -17v2 = 0 18v + -32v3 = 0 Solving 18v + -32v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2v'. 2v(9 + -16v2) = 0 Factor a difference between two squares. 2v((3 + 4v)(3 + -4v)) = 0 Ignore the factor 2.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 '(3 + 4v)' equal to zero and attempt to solve: Simplifying 3 + 4v = 0 Solving 3 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4v = 0 + -3 4v = 0 + -3 Combine like terms: 0 + -3 = -3 4v = -3 Divide each side by '4'. v = -0.75 Simplifying v = -0.75Subproblem 3
Set the factor '(3 + -4v)' equal to zero and attempt to solve: Simplifying 3 + -4v = 0 Solving 3 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4v = 0 + -3 -4v = 0 + -3 Combine like terms: 0 + -3 = -3 -4v = -3 Divide each side by '-4'. v = 0.75 Simplifying v = 0.75Solution
v = {0, -0.75, 0.75}
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