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Simplifying (a + b)(2a + b) = 0 Multiply (a + b) * (2a + b) (a(2a + b) + b(2a + b)) = 0 ((2a * a + b * a) + b(2a + b)) = 0 Reorder the terms: ((ab + 2a2) + b(2a + b)) = 0 ((ab + 2a2) + b(2a + b)) = 0 (ab + 2a2 + (2a * b + b * b)) = 0 (ab + 2a2 + (2ab + b2)) = 0 Reorder the terms: (ab + 2ab + 2a2 + b2) = 0 Combine like terms: ab + 2ab = 3ab (3ab + 2a2 + b2) = 0 Solving 3ab + 2a2 + b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + b)(a + b) = 0Subproblem 1
Set the factor '(2a + b)' equal to zero and attempt to solve: Simplifying 2a + b = 0 Solving 2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5bSubproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSolution
a = {-0.5b, -1b}
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