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Simplifying a2 = 45 + -4a Solving a2 = 45 + -4a Solving for variable 'a'. Reorder the terms: -45 + 4a + a2 = 45 + -4a + -45 + 4a Reorder the terms: -45 + 4a + a2 = 45 + -45 + -4a + 4a Combine like terms: 45 + -45 = 0 -45 + 4a + a2 = 0 + -4a + 4a -45 + 4a + a2 = -4a + 4a Combine like terms: -4a + 4a = 0 -45 + 4a + a2 = 0 Factor a trinomial. (-9 + -1a)(5 + -1a) = 0Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve: Simplifying -9 + -1a = 0 Solving -9 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1a = 0 + 9 -1a = 0 + 9 Combine like terms: 0 + 9 = 9 -1a = 9 Divide each side by '-1'. a = -9 Simplifying a = -9Subproblem 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 = {-9, 5}
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