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Simplifying 18w2 + 24wf + 8f2 = 0 Reorder the terms: 24fw + 8f2 + 18w2 = 0 Solving 24fw + 8f2 + 18w2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '2'. 2(12fw + 4f2 + 9w2) = 0 Factor a trinomial. 2((2f + 3w)(2f + 3w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2f + 3w)' equal to zero and attempt to solve: Simplifying 2f + 3w = 0 Solving 2f + 3w = 0 Move all terms containing f to the left, all other terms to the right. Add '-3w' to each side of the equation. 2f + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 2f + 0 = 0 + -3w 2f = 0 + -3w Remove the zero: 2f = -3w Divide each side by '2'. f = -1.5w Simplifying f = -1.5wSubproblem 2
Set the factor '(2f + 3w)' equal to zero and attempt to solve: Simplifying 2f + 3w = 0 Solving 2f + 3w = 0 Move all terms containing f to the left, all other terms to the right. Add '-3w' to each side of the equation. 2f + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 2f + 0 = 0 + -3w 2f = 0 + -3w Remove the zero: 2f = -3w Divide each side by '2'. f = -1.5w Simplifying f = -1.5wSolution
f = {-1.5w, -1.5w}
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