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Simplifying 20a2 + 11aw + -3w2 = 0 Reorder the terms: 11aw + 20a2 + -3w2 = 0 Solving 11aw + 20a2 + -3w2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -1w)(4a + 3w) = 0Subproblem 1
Set the factor '(5a + -1w)' equal to zero and attempt to solve: Simplifying 5a + -1w = 0 Solving 5a + -1w = 0 Move all terms containing a to the left, all other terms to the right. Add 'w' to each side of the equation. 5a + -1w + w = 0 + w Combine like terms: -1w + w = 0 5a + 0 = 0 + w 5a = 0 + w Remove the zero: 5a = w Divide each side by '5'. a = 0.2w Simplifying a = 0.2wSubproblem 2
Set the factor '(4a + 3w)' equal to zero and attempt to solve: Simplifying 4a + 3w = 0 Solving 4a + 3w = 0 Move all terms containing a to the left, all other terms to the right. Add '-3w' to each side of the equation. 4a + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 4a + 0 = 0 + -3w 4a = 0 + -3w Remove the zero: 4a = -3w Divide each side by '4'. a = -0.75w Simplifying a = -0.75wSolution
a = {0.2w, -0.75w}
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