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Simplifying 7a(5a + -4) + -1 = 14 + -8a Reorder the terms: 7a(-4 + 5a) + -1 = 14 + -8a (-4 * 7a + 5a * 7a) + -1 = 14 + -8a (-28a + 35a2) + -1 = 14 + -8a Reorder the terms: -1 + -28a + 35a2 = 14 + -8a Solving -1 + -28a + 35a2 = 14 + -8a Solving for variable 'a'. Reorder the terms: -1 + -14 + -28a + 8a + 35a2 = 14 + -8a + -14 + 8a Combine like terms: -1 + -14 = -15 -15 + -28a + 8a + 35a2 = 14 + -8a + -14 + 8a Combine like terms: -28a + 8a = -20a -15 + -20a + 35a2 = 14 + -8a + -14 + 8a Reorder the terms: -15 + -20a + 35a2 = 14 + -14 + -8a + 8a Combine like terms: 14 + -14 = 0 -15 + -20a + 35a2 = 0 + -8a + 8a -15 + -20a + 35a2 = -8a + 8a Combine like terms: -8a + 8a = 0 -15 + -20a + 35a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + -4a + 7a2) = 0 Factor a trinomial. 5((-3 + -7a)(1 + -1a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -7a)' equal to zero and attempt to solve: Simplifying -3 + -7a = 0 Solving -3 + -7a = 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 + -7a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7a = 0 + 3 -7a = 0 + 3 Combine like terms: 0 + 3 = 3 -7a = 3 Divide each side by '-7'. a = -0.4285714286 Simplifying a = -0.4285714286Subproblem 2
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 = 1Solution
a = {-0.4285714286, 1}
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