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Simplifying 5a2 + 45ab + 100b2 = 0 Reorder the terms: 45ab + 5a2 + 100b2 = 0 Solving 45ab + 5a2 + 100b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(9ab + a2 + 20b2) = 0 Factor a trinomial. 5((a + 4b)(a + 5b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(a + 4b)' equal to zero and attempt to solve: Simplifying a + 4b = 0 Solving a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 a + 0 = 0 + -4b a = 0 + -4b Remove the zero: a = -4b Simplifying a = -4bSubproblem 2
Set the factor '(a + 5b)' equal to zero and attempt to solve: Simplifying a + 5b = 0 Solving a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 a + 0 = 0 + -5b a = 0 + -5b Remove the zero: a = -5b Simplifying a = -5bSolution
a = {-4b, -5b}
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