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Simplifying (3a + 13b)(3a + 13b) = 0 Multiply (3a + 13b) * (3a + 13b) (3a * (3a + 13b) + 13b * (3a + 13b)) = 0 ((3a * 3a + 13b * 3a) + 13b * (3a + 13b)) = 0 Reorder the terms: ((39ab + 9a2) + 13b * (3a + 13b)) = 0 ((39ab + 9a2) + 13b * (3a + 13b)) = 0 (39ab + 9a2 + (3a * 13b + 13b * 13b)) = 0 (39ab + 9a2 + (39ab + 169b2)) = 0 Reorder the terms: (39ab + 39ab + 9a2 + 169b2) = 0 Combine like terms: 39ab + 39ab = 78ab (78ab + 9a2 + 169b2) = 0 Solving 78ab + 9a2 + 169b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + 13b)(3a + 13b) = 0Subproblem 1
Set the factor '(3a + 13b)' equal to zero and attempt to solve: Simplifying 3a + 13b = 0 Solving 3a + 13b = 0 Move all terms containing a to the left, all other terms to the right. Add '-13b' to each side of the equation. 3a + 13b + -13b = 0 + -13b Combine like terms: 13b + -13b = 0 3a + 0 = 0 + -13b 3a = 0 + -13b Remove the zero: 3a = -13b Divide each side by '3'. a = -4.333333333b Simplifying a = -4.333333333bSubproblem 2
Set the factor '(3a + 13b)' equal to zero and attempt to solve: Simplifying 3a + 13b = 0 Solving 3a + 13b = 0 Move all terms containing a to the left, all other terms to the right. Add '-13b' to each side of the equation. 3a + 13b + -13b = 0 + -13b Combine like terms: 13b + -13b = 0 3a + 0 = 0 + -13b 3a = 0 + -13b Remove the zero: 3a = -13b Divide each side by '3'. a = -4.333333333b Simplifying a = -4.333333333bSolution
a = {-4.333333333b, -4.333333333b}
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