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Simplifying 5a2 + 10ab + 5b2 = 0 Reorder the terms: 10ab + 5a2 + 5b2 = 0 Solving 10ab + 5a2 + 5b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(2ab + a2 + b2) = 0 Factor a trinomial. 5((a + b)(a + b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSubproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSolution
a = {-1b, -1b}
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