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