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Simplifying 2a2 + -24a + 72 = 98 Reorder the terms: 72 + -24a + 2a2 = 98 Solving 72 + -24a + 2a2 = 98 Solving for variable 'a'. Reorder the terms: 72 + -98 + -24a + 2a2 = 98 + -98 Combine like terms: 72 + -98 = -26 -26 + -24a + 2a2 = 98 + -98 Combine like terms: 98 + -98 = 0 -26 + -24a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -12a + a2) = 0 Factor a trinomial. 2((-1 + -1a)(13 + -1a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1a)' equal to zero and attempt to solve: Simplifying -1 + -1a = 0 Solving -1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1a = 0 + 1 -1a = 0 + 1 Combine like terms: 0 + 1 = 1 -1a = 1 Divide each side by '-1'. a = -1 Simplifying a = -1Subproblem 2
Set the factor '(13 + -1a)' equal to zero and attempt to solve: Simplifying 13 + -1a = 0 Solving 13 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1a = 0 + -13 -1a = 0 + -13 Combine like terms: 0 + -13 = -13 -1a = -13 Divide each side by '-1'. a = 13 Simplifying a = 13Solution
a = {-1, 13}
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