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Simplifying 81a2 + 180ab + 100b2 = 0 Reorder the terms: 180ab + 81a2 + 100b2 = 0 Solving 180ab + 81a2 + 100b2 = 0 Solving for variable 'a'. Factor a trinomial. (9a + 10b)(9a + 10b) = 0Subproblem 1
Set the factor '(9a + 10b)' equal to zero and attempt to solve: Simplifying 9a + 10b = 0 Solving 9a + 10b = 0 Move all terms containing a to the left, all other terms to the right. Add '-10b' to each side of the equation. 9a + 10b + -10b = 0 + -10b Combine like terms: 10b + -10b = 0 9a + 0 = 0 + -10b 9a = 0 + -10b Remove the zero: 9a = -10b Divide each side by '9'. a = -1.111111111b Simplifying a = -1.111111111bSubproblem 2
Set the factor '(9a + 10b)' equal to zero and attempt to solve: Simplifying 9a + 10b = 0 Solving 9a + 10b = 0 Move all terms containing a to the left, all other terms to the right. Add '-10b' to each side of the equation. 9a + 10b + -10b = 0 + -10b Combine like terms: 10b + -10b = 0 9a + 0 = 0 + -10b 9a = 0 + -10b Remove the zero: 9a = -10b Divide each side by '9'. a = -1.111111111b Simplifying a = -1.111111111bSolution
a = {-1.111111111b, -1.111111111b}
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