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