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Simplifying 30a2 + 5ab + -25b2 = 0 Reorder the terms: 5ab + 30a2 + -25b2 = 0 Solving 5ab + 30a2 + -25b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(ab + 6a2 + -5b2) = 0 Factor a trinomial. 5((6a + -5b)(a + b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6a + -5b)' equal to zero and attempt to solve: Simplifying 6a + -5b = 0 Solving 6a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 6a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 6a + 0 = 0 + 5b 6a = 0 + 5b Remove the zero: 6a = 5b Divide each side by '6'. a = 0.8333333333b Simplifying a = 0.8333333333bSubproblem 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 = {0.8333333333b, -1b}
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