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Simplifying (-9a + -7)(14a + -11) + -1(-12a + 15)(-9a + -7) = 0 Reorder the terms: (-7 + -9a)(14a + -11) + -1(-12a + 15)(-9a + -7) = 0 Reorder the terms: (-7 + -9a)(-11 + 14a) + -1(-12a + 15)(-9a + -7) = 0 Multiply (-7 + -9a) * (-11 + 14a) (-7(-11 + 14a) + -9a * (-11 + 14a)) + -1(-12a + 15)(-9a + -7) = 0 ((-11 * -7 + 14a * -7) + -9a * (-11 + 14a)) + -1(-12a + 15)(-9a + -7) = 0 ((77 + -98a) + -9a * (-11 + 14a)) + -1(-12a + 15)(-9a + -7) = 0 (77 + -98a + (-11 * -9a + 14a * -9a)) + -1(-12a + 15)(-9a + -7) = 0 (77 + -98a + (99a + -126a2)) + -1(-12a + 15)(-9a + -7) = 0 Combine like terms: -98a + 99a = 1a (77 + 1a + -126a2) + -1(-12a + 15)(-9a + -7) = 0 Reorder the terms: 77 + 1a + -126a2 + -1(15 + -12a)(-9a + -7) = 0 Reorder the terms: 77 + 1a + -126a2 + -1(15 + -12a)(-7 + -9a) = 0 Multiply (15 + -12a) * (-7 + -9a) 77 + 1a + -126a2 + -1(15(-7 + -9a) + -12a * (-7 + -9a)) = 0 77 + 1a + -126a2 + -1((-7 * 15 + -9a * 15) + -12a * (-7 + -9a)) = 0 77 + 1a + -126a2 + -1((-105 + -135a) + -12a * (-7 + -9a)) = 0 77 + 1a + -126a2 + -1(-105 + -135a + (-7 * -12a + -9a * -12a)) = 0 77 + 1a + -126a2 + -1(-105 + -135a + (84a + 108a2)) = 0 Combine like terms: -135a + 84a = -51a 77 + 1a + -126a2 + -1(-105 + -51a + 108a2) = 0 77 + 1a + -126a2 + (-105 * -1 + -51a * -1 + 108a2 * -1) = 0 77 + 1a + -126a2 + (105 + 51a + -108a2) = 0 Reorder the terms: 77 + 105 + 1a + 51a + -126a2 + -108a2 = 0 Combine like terms: 77 + 105 = 182 182 + 1a + 51a + -126a2 + -108a2 = 0 Combine like terms: 1a + 51a = 52a 182 + 52a + -126a2 + -108a2 = 0 Combine like terms: -126a2 + -108a2 = -234a2 182 + 52a + -234a2 = 0 Solving 182 + 52a + -234a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '26'. 26(7 + 2a + -9a2) = 0 Factor a trinomial. 26((1 + -1a)(7 + 9a)) = 0 Ignore the factor 26.Subproblem 1
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 = 1Subproblem 2
Set the factor '(7 + 9a)' equal to zero and attempt to solve: Simplifying 7 + 9a = 0 Solving 7 + 9a = 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 + 9a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9a = 0 + -7 9a = 0 + -7 Combine like terms: 0 + -7 = -7 9a = -7 Divide each side by '9'. a = -0.7777777778 Simplifying a = -0.7777777778Solution
a = {1, -0.7777777778}
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