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Simplifying 20a2 + 57ab + 27b2 = 0 Reorder the terms: 57ab + 20a2 + 27b2 = 0 Solving 57ab + 20a2 + 27b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + 3b)(4a + 9b) = 0Subproblem 1
Set the factor '(5a + 3b)' equal to zero and attempt to solve: Simplifying 5a + 3b = 0 Solving 5a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 5a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 5a + 0 = 0 + -3b 5a = 0 + -3b Remove the zero: 5a = -3b Divide each side by '5'. a = -0.6b Simplifying a = -0.6bSubproblem 2
Set the factor '(4a + 9b)' equal to zero and attempt to solve: Simplifying 4a + 9b = 0 Solving 4a + 9b = 0 Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. 4a + 9b + -9b = 0 + -9b Combine like terms: 9b + -9b = 0 4a + 0 = 0 + -9b 4a = 0 + -9b Remove the zero: 4a = -9b Divide each side by '4'. a = -2.25b Simplifying a = -2.25bSolution
a = {-0.6b, -2.25b}
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