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Simplifying 48a2 + 37ab + -36b2 = 0 Reorder the terms: 37ab + 48a2 + -36b2 = 0 Solving 37ab + 48a2 + -36b2 = 0 Solving for variable 'a'. Factor a trinomial. (16a + -9b)(3a + 4b) = 0Subproblem 1
Set the factor '(16a + -9b)' equal to zero and attempt to solve: Simplifying 16a + -9b = 0 Solving 16a + -9b = 0 Move all terms containing a to the left, all other terms to the right. Add '9b' to each side of the equation. 16a + -9b + 9b = 0 + 9b Combine like terms: -9b + 9b = 0 16a + 0 = 0 + 9b 16a = 0 + 9b Remove the zero: 16a = 9b Divide each side by '16'. a = 0.5625b Simplifying a = 0.5625bSubproblem 2
Set the factor '(3a + 4b)' equal to zero and attempt to solve: Simplifying 3a + 4b = 0 Solving 3a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 3a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 3a + 0 = 0 + -4b 3a = 0 + -4b Remove the zero: 3a = -4b Divide each side by '3'. a = -1.333333333b Simplifying a = -1.333333333bSolution
a = {0.5625b, -1.333333333b}
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