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Simplifying 10a2 + -33aw + 20w2 = 0 Reorder the terms: -33aw + 10a2 + 20w2 = 0 Solving -33aw + 10a2 + 20w2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -5w)(5a + -4w) = 0Subproblem 1
Set the factor '(2a + -5w)' equal to zero and attempt to solve: Simplifying 2a + -5w = 0 Solving 2a + -5w = 0 Move all terms containing a to the left, all other terms to the right. Add '5w' to each side of the equation. 2a + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 2a + 0 = 0 + 5w 2a = 0 + 5w Remove the zero: 2a = 5w Divide each side by '2'. a = 2.5w Simplifying a = 2.5wSubproblem 2
Set the factor '(5a + -4w)' equal to zero and attempt to solve: Simplifying 5a + -4w = 0 Solving 5a + -4w = 0 Move all terms containing a to the left, all other terms to the right. Add '4w' to each side of the equation. 5a + -4w + 4w = 0 + 4w Combine like terms: -4w + 4w = 0 5a + 0 = 0 + 4w 5a = 0 + 4w Remove the zero: 5a = 4w Divide each side by '5'. a = 0.8w Simplifying a = 0.8wSolution
a = {2.5w, 0.8w}
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