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Simplifying a3 + -1a + a2 + -5 = a3 + -1a2 + a2 + -1a + 2a + -2 Reorder the terms: -5 + -1a + a2 + a3 = a3 + -1a2 + a2 + -1a + 2a + -2 Reorder the terms: -5 + -1a + a2 + a3 = -2 + -1a + 2a + -1a2 + a2 + a3 Combine like terms: -1a + 2a = 1a -5 + -1a + a2 + a3 = -2 + 1a + -1a2 + a2 + a3 Combine like terms: -1a2 + a2 = 0 -5 + -1a + a2 + a3 = -2 + 1a + 0 + a3 -5 + -1a + a2 + a3 = -2 + 1a + a3 Add '-1a3' to each side of the equation. -5 + -1a + a2 + a3 + -1a3 = -2 + 1a + a3 + -1a3 Combine like terms: a3 + -1a3 = 0 -5 + -1a + a2 + 0 = -2 + 1a + a3 + -1a3 -5 + -1a + a2 = -2 + 1a + a3 + -1a3 Combine like terms: a3 + -1a3 = 0 -5 + -1a + a2 = -2 + 1a + 0 -5 + -1a + a2 = -2 + 1a Solving -5 + -1a + a2 = -2 + 1a Solving for variable 'a'. Reorder the terms: -5 + 2 + -1a + -1a + a2 = -2 + 1a + 2 + -1a Combine like terms: -5 + 2 = -3 -3 + -1a + -1a + a2 = -2 + 1a + 2 + -1a Combine like terms: -1a + -1a = -2a -3 + -2a + a2 = -2 + 1a + 2 + -1a Reorder the terms: -3 + -2a + a2 = -2 + 2 + 1a + -1a Combine like terms: -2 + 2 = 0 -3 + -2a + a2 = 0 + 1a + -1a -3 + -2a + a2 = 1a + -1a Combine like terms: 1a + -1a = 0 -3 + -2a + a2 = 0 Factor a trinomial. (-1 + -1a)(3 + -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 '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-1, 3}
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