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Simplifying 5a2 + -8a + -31 = -10 Reorder the terms: -31 + -8a + 5a2 = -10 Solving -31 + -8a + 5a2 = -10 Solving for variable 'a'. Reorder the terms: -31 + 10 + -8a + 5a2 = -10 + 10 Combine like terms: -31 + 10 = -21 -21 + -8a + 5a2 = -10 + 10 Combine like terms: -10 + 10 = 0 -21 + -8a + 5a2 = 0 Factor a trinomial. (-7 + -5a)(3 + -1a) = 0Subproblem 1
Set the factor '(-7 + -5a)' equal to zero and attempt to solve: Simplifying -7 + -5a = 0 Solving -7 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5a = 0 + 7 -5a = 0 + 7 Combine like terms: 0 + 7 = 7 -5a = 7 Divide each side by '-5'. a = -1.4 Simplifying a = -1.4Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-1.4, 3}
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