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Simplifying 4a2 + 16ab + 16b2 = 0 Reorder the terms: 16ab + 4a2 + 16b2 = 0 Solving 16ab + 4a2 + 16b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(4ab + a2 + 4b2) = 0 Factor a trinomial. 4((a + 2b)(a + 2b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(a + 2b)' equal to zero and attempt to solve: Simplifying a + 2b = 0 Solving a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 a + 0 = 0 + -2b a = 0 + -2b Remove the zero: a = -2b Simplifying a = -2bSubproblem 2
Set the factor '(a + 2b)' equal to zero and attempt to solve: Simplifying a + 2b = 0 Solving a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 a + 0 = 0 + -2b a = 0 + -2b Remove the zero: a = -2b Simplifying a = -2bSolution
a = {-2b, -2b}
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