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Simplifying (9a + -1b)(9a + -1b) = 0 Multiply (9a + -1b) * (9a + -1b) (9a * (9a + -1b) + -1b * (9a + -1b)) = 0 ((9a * 9a + -1b * 9a) + -1b * (9a + -1b)) = 0 Reorder the terms: ((-9ab + 81a2) + -1b * (9a + -1b)) = 0 ((-9ab + 81a2) + -1b * (9a + -1b)) = 0 (-9ab + 81a2 + (9a * -1b + -1b * -1b)) = 0 (-9ab + 81a2 + (-9ab + 1b2)) = 0 Reorder the terms: (-9ab + -9ab + 81a2 + 1b2) = 0 Combine like terms: -9ab + -9ab = -18ab (-18ab + 81a2 + 1b2) = 0 Solving -18ab + 81a2 + 1b2 = 0 Solving for variable 'a'. Factor a trinomial. (9a + -1b)(9a + -1b) = 0Subproblem 1
Set the factor '(9a + -1b)' equal to zero and attempt to solve: Simplifying 9a + -1b = 0 Solving 9a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 9a + -1b + b = 0 + b Combine like terms: -1b + b = 0 9a + 0 = 0 + b 9a = 0 + b Remove the zero: 9a = b Divide each side by '9'. a = 0.1111111111b Simplifying a = 0.1111111111bSubproblem 2
Set the factor '(9a + -1b)' equal to zero and attempt to solve: Simplifying 9a + -1b = 0 Solving 9a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 9a + -1b + b = 0 + b Combine like terms: -1b + b = 0 9a + 0 = 0 + b 9a = 0 + b Remove the zero: 9a = b Divide each side by '9'. a = 0.1111111111b Simplifying a = 0.1111111111bSolution
a = {0.1111111111b, 0.1111111111b}
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