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Simplifying (9a + 4b)(-9a + -5b) = 0 Multiply (9a + 4b) * (-9a + -5b) (9a * (-9a + -5b) + 4b * (-9a + -5b)) = 0 ((-9a * 9a + -5b * 9a) + 4b * (-9a + -5b)) = 0 Reorder the terms: ((-45ab + -81a2) + 4b * (-9a + -5b)) = 0 ((-45ab + -81a2) + 4b * (-9a + -5b)) = 0 (-45ab + -81a2 + (-9a * 4b + -5b * 4b)) = 0 (-45ab + -81a2 + (-36ab + -20b2)) = 0 Reorder the terms: (-45ab + -36ab + -81a2 + -20b2) = 0 Combine like terms: -45ab + -36ab = -81ab (-81ab + -81a2 + -20b2) = 0 Solving -81ab + -81a2 + -20b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(81ab + 81a2 + 20b2) = 0 Factor a trinomial. -1((9a + 4b)(9a + 5b)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9a + 4b)' equal to zero and attempt to solve: Simplifying 9a + 4b = 0 Solving 9a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 9a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 9a + 0 = 0 + -4b 9a = 0 + -4b Remove the zero: 9a = -4b Divide each side by '9'. a = -0.4444444444b Simplifying a = -0.4444444444bSubproblem 2
Set the factor '(9a + 5b)' equal to zero and attempt to solve: Simplifying 9a + 5b = 0 Solving 9a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 9a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 9a + 0 = 0 + -5b 9a = 0 + -5b Remove the zero: 9a = -5b Divide each side by '9'. a = -0.5555555556b Simplifying a = -0.5555555556bSolution
a = {-0.4444444444b, -0.5555555556b}
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