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Simplifying 42a2 + -24 = -27a Reorder the terms: -24 + 42a2 = -27a Solving -24 + 42a2 = -27a Solving for variable 'a'. Reorder the terms: -24 + 27a + 42a2 = -27a + 27a Combine like terms: -27a + 27a = 0 -24 + 27a + 42a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 9a + 14a2) = 0 Factor a trinomial. 3((-8 + -7a)(1 + -2a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -7a)' equal to zero and attempt to solve: Simplifying -8 + -7a = 0 Solving -8 + -7a = 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 + -7a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7a = 0 + 8 -7a = 0 + 8 Combine like terms: 0 + 8 = 8 -7a = 8 Divide each side by '-7'. a = -1.142857143 Simplifying a = -1.142857143Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {-1.142857143, 0.5}
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