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Simplifying 18a2 + 78ab = -84b2 Reorder the terms: 78ab + 18a2 = -84b2 Solving 78ab + 18a2 = -84b2 Solving for variable 'a'. Combine like terms: -84b2 + 84b2 = 0 78ab + 18a2 + 84b2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(13ab + 3a2 + 14b2) = 0 Factor a trinomial. 6((a + 2b)(3a + 7b)) = 0 Ignore the factor 6.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 '(3a + 7b)' equal to zero and attempt to solve: Simplifying 3a + 7b = 0 Solving 3a + 7b = 0 Move all terms containing a to the left, all other terms to the right. Add '-7b' to each side of the equation. 3a + 7b + -7b = 0 + -7b Combine like terms: 7b + -7b = 0 3a + 0 = 0 + -7b 3a = 0 + -7b Remove the zero: 3a = -7b Divide each side by '3'. a = -2.333333333b Simplifying a = -2.333333333bSolution
a = {-2b, -2.333333333b}
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