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Simplifying 20a2 + 47ab + 24b2 = 0 Reorder the terms: 47ab + 20a2 + 24b2 = 0 Solving 47ab + 20a2 + 24b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + 3b)(5a + 8b) = 0Subproblem 1
Set the factor '(4a + 3b)' equal to zero and attempt to solve: Simplifying 4a + 3b = 0 Solving 4a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 4a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 4a + 0 = 0 + -3b 4a = 0 + -3b Remove the zero: 4a = -3b Divide each side by '4'. a = -0.75b Simplifying a = -0.75bSubproblem 2
Set the factor '(5a + 8b)' equal to zero and attempt to solve: Simplifying 5a + 8b = 0 Solving 5a + 8b = 0 Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 5a + 8b + -8b = 0 + -8b Combine like terms: 8b + -8b = 0 5a + 0 = 0 + -8b 5a = 0 + -8b Remove the zero: 5a = -8b Divide each side by '5'. a = -1.6b Simplifying a = -1.6bSolution
a = {-0.75b, -1.6b}
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