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