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Simplifying (17 + a)(17 + a) = 2209 Multiply (17 + a) * (17 + a) (17(17 + a) + a(17 + a)) = 2209 ((17 * 17 + a * 17) + a(17 + a)) = 2209 ((289 + 17a) + a(17 + a)) = 2209 (289 + 17a + (17 * a + a * a)) = 2209 (289 + 17a + (17a + a2)) = 2209 Combine like terms: 17a + 17a = 34a (289 + 34a + a2) = 2209 Solving 289 + 34a + a2 = 2209 Solving for variable 'a'. Reorder the terms: 289 + -2209 + 34a + a2 = 2209 + -2209 Combine like terms: 289 + -2209 = -1920 -1920 + 34a + a2 = 2209 + -2209 Combine like terms: 2209 + -2209 = 0 -1920 + 34a + a2 = 0 Factor a trinomial. (-64 + -1a)(30 + -1a) = 0Subproblem 1
Set the factor '(-64 + -1a)' equal to zero and attempt to solve: Simplifying -64 + -1a = 0 Solving -64 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '64' to each side of the equation. -64 + 64 + -1a = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -1a = 0 + 64 -1a = 0 + 64 Combine like terms: 0 + 64 = 64 -1a = 64 Divide each side by '-1'. a = -64 Simplifying a = -64Subproblem 2
Set the factor '(30 + -1a)' equal to zero and attempt to solve: Simplifying 30 + -1a = 0 Solving 30 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1a = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1a = 0 + -30 -1a = 0 + -30 Combine like terms: 0 + -30 = -30 -1a = -30 Divide each side by '-1'. a = 30 Simplifying a = 30Solution
a = {-64, 30}
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