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Simplifying 42a2 + 146a + 112 = 0 Reorder the terms: 112 + 146a + 42a2 = 0 Solving 112 + 146a + 42a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(56 + 73a + 21a2) = 0 Factor a trinomial. 2((7 + 3a)(8 + 7a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 3a)' equal to zero and attempt to solve: Simplifying 7 + 3a = 0 Solving 7 + 3a = 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 + 3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3a = 0 + -7 3a = 0 + -7 Combine like terms: 0 + -7 = -7 3a = -7 Divide each side by '3'. a = -2.333333333 Simplifying a = -2.333333333Subproblem 2
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 = -1.142857143Solution
a = {-2.333333333, -1.142857143}
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