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Simplifying (a)(a + 1) = (a + (a + 1) + 19) Reorder the terms: a(1 + a) = (a + (a + 1) + 19) (1 * a + a * a) = (a + (a + 1) + 19) (1a + a2) = (a + (a + 1) + 19) Reorder the terms: 1a + a2 = (a + (1 + a) + 19) Remove parenthesis around (1 + a) 1a + a2 = (a + 1 + a + 19) Reorder the terms: 1a + a2 = (1 + 19 + a + a) Combine like terms: 1 + 19 = 20 1a + a2 = (20 + a + a) Combine like terms: a + a = 2a 1a + a2 = (20 + 2a) Remove parenthesis around (20 + 2a) 1a + a2 = 20 + 2a Solving 1a + a2 = 20 + 2a Solving for variable 'a'. Reorder the terms: -20 + 1a + -2a + a2 = 20 + 2a + -20 + -2a Combine like terms: 1a + -2a = -1a -20 + -1a + a2 = 20 + 2a + -20 + -2a Reorder the terms: -20 + -1a + a2 = 20 + -20 + 2a + -2a Combine like terms: 20 + -20 = 0 -20 + -1a + a2 = 0 + 2a + -2a -20 + -1a + a2 = 2a + -2a Combine like terms: 2a + -2a = 0 -20 + -1a + a2 = 0 Factor a trinomial. (-4 + -1a)(5 + -1a) = 0Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {-4, 5}
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