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Simplifying 16a2 + -4ab + -20b2 = 0 Reorder the terms: -4ab + 16a2 + -20b2 = 0 Solving -4ab + 16a2 + -20b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1ab + 4a2 + -5b2) = 0 Factor a trinomial. 4((4a + -5b)(a + b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4a + -5b)' equal to zero and attempt to solve: Simplifying 4a + -5b = 0 Solving 4a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 4a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 4a + 0 = 0 + 5b 4a = 0 + 5b Remove the zero: 4a = 5b Divide each side by '4'. a = 1.25b Simplifying a = 1.25bSubproblem 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 = {1.25b, -1b}
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