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Simplifying 10a2 + -13a + -22 = 8 Reorder the terms: -22 + -13a + 10a2 = 8 Solving -22 + -13a + 10a2 = 8 Solving for variable 'a'. Reorder the terms: -22 + -8 + -13a + 10a2 = 8 + -8 Combine like terms: -22 + -8 = -30 -30 + -13a + 10a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -30 + -13a + 10a2 = 0 Factor a trinomial. (-6 + -5a)(5 + -2a) = 0Subproblem 1
Set the factor '(-6 + -5a)' equal to zero and attempt to solve: Simplifying -6 + -5a = 0 Solving -6 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5a = 0 + 6 -5a = 0 + 6 Combine like terms: 0 + 6 = 6 -5a = 6 Divide each side by '-5'. a = -1.2 Simplifying a = -1.2Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 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 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5Solution
a = {-1.2, 2.5}
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