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Simplifying (a + 1)(a + 1) = 25 Reorder the terms: (1 + a)(a + 1) = 25 Reorder the terms: (1 + a)(1 + a) = 25 Multiply (1 + a) * (1 + a) (1(1 + a) + a(1 + a)) = 25 ((1 * 1 + a * 1) + a(1 + a)) = 25 ((1 + 1a) + a(1 + a)) = 25 (1 + 1a + (1 * a + a * a)) = 25 (1 + 1a + (1a + a2)) = 25 Combine like terms: 1a + 1a = 2a (1 + 2a + a2) = 25 Solving 1 + 2a + a2 = 25 Solving for variable 'a'. Reorder the terms: 1 + -25 + 2a + a2 = 25 + -25 Combine like terms: 1 + -25 = -24 -24 + 2a + a2 = 25 + -25 Combine like terms: 25 + -25 = 0 -24 + 2a + a2 = 0 Factor a trinomial. (-6 + -1a)(4 + -1a) = 0Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve: Simplifying -6 + -1a = 0 Solving -6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1a = 0 + 6 -1a = 0 + 6 Combine like terms: 0 + 6 = 6 -1a = 6 Divide each side by '-1'. a = -6 Simplifying a = -6Subproblem 2
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 = 4Solution
a = {-6, 4}
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