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Simplifying a2 = 80 + 2a Solving a2 = 80 + 2a Solving for variable 'a'. Reorder the terms: -80 + -2a + a2 = 80 + 2a + -80 + -2a Reorder the terms: -80 + -2a + a2 = 80 + -80 + 2a + -2a Combine like terms: 80 + -80 = 0 -80 + -2a + a2 = 0 + 2a + -2a -80 + -2a + a2 = 2a + -2a Combine like terms: 2a + -2a = 0 -80 + -2a + a2 = 0 Factor a trinomial. (-8 + -1a)(10 + -1a) = 0Subproblem 1
Set the factor '(-8 + -1a)' equal to zero and attempt to solve: Simplifying -8 + -1a = 0 Solving -8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1a = 0 + 8 -1a = 0 + 8 Combine like terms: 0 + 8 = 8 -1a = 8 Divide each side by '-1'. a = -8 Simplifying a = -8Subproblem 2
Set the factor '(10 + -1a)' equal to zero and attempt to solve: Simplifying 10 + -1a = 0 Solving 10 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1a = 0 + -10 -1a = 0 + -10 Combine like terms: 0 + -10 = -10 -1a = -10 Divide each side by '-1'. a = 10 Simplifying a = 10Solution
a = {-8, 10}
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