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Simplifying 81v4 + -900v2 = 0 Reorder the terms: -900v2 + 81v4 = 0 Solving -900v2 + 81v4 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '9v2'. 9v2(-100 + 9v2) = 0 Factor a difference between two squares. 9v2((10 + 3v)(-10 + 3v)) = 0 Ignore the factor 9.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 '(10 + 3v)' equal to zero and attempt to solve: Simplifying 10 + 3v = 0 Solving 10 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3v = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3v = 0 + -10 3v = 0 + -10 Combine like terms: 0 + -10 = -10 3v = -10 Divide each side by '3'. v = -3.333333333 Simplifying v = -3.333333333Subproblem 3
Set the factor '(-10 + 3v)' equal to zero and attempt to solve: Simplifying -10 + 3v = 0 Solving -10 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 3v = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3v = 0 + 10 3v = 0 + 10 Combine like terms: 0 + 10 = 10 3v = 10 Divide each side by '3'. v = 3.333333333 Simplifying v = 3.333333333Solution
v = {0, -3.333333333, 3.333333333}
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