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