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Simplifying (3a + b)(3a + b) = 0 Multiply (3a + b) * (3a + b) (3a * (3a + b) + b(3a + b)) = 0 ((3a * 3a + b * 3a) + b(3a + b)) = 0 Reorder the terms: ((3ab + 9a2) + b(3a + b)) = 0 ((3ab + 9a2) + b(3a + b)) = 0 (3ab + 9a2 + (3a * b + b * b)) = 0 (3ab + 9a2 + (3ab + b2)) = 0 Reorder the terms: (3ab + 3ab + 9a2 + b2) = 0 Combine like terms: 3ab + 3ab = 6ab (6ab + 9a2 + b2) = 0 Solving 6ab + 9a2 + b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + b)(3a + b) = 0Subproblem 1
Set the factor '(3a + b)' equal to zero and attempt to solve: Simplifying 3a + b = 0 Solving 3a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 3a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 3a + 0 = 0 + -1b 3a = 0 + -1b Remove the zero: 3a = -1b Divide each side by '3'. a = -0.3333333333b Simplifying a = -0.3333333333bSubproblem 2
Set the factor '(3a + b)' equal to zero and attempt to solve: Simplifying 3a + b = 0 Solving 3a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 3a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 3a + 0 = 0 + -1b 3a = 0 + -1b Remove the zero: 3a = -1b Divide each side by '3'. a = -0.3333333333b Simplifying a = -0.3333333333bSolution
a = {-0.3333333333b, -0.3333333333b}
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