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Simplifying (7a + 9)(a + -8) + (14a + -16)(a + -8) = 0 Reorder the terms: (9 + 7a)(a + -8) + (14a + -16)(a + -8) = 0 Reorder the terms: (9 + 7a)(-8 + a) + (14a + -16)(a + -8) = 0 Multiply (9 + 7a) * (-8 + a) (9(-8 + a) + 7a * (-8 + a)) + (14a + -16)(a + -8) = 0 ((-8 * 9 + a * 9) + 7a * (-8 + a)) + (14a + -16)(a + -8) = 0 ((-72 + 9a) + 7a * (-8 + a)) + (14a + -16)(a + -8) = 0 (-72 + 9a + (-8 * 7a + a * 7a)) + (14a + -16)(a + -8) = 0 (-72 + 9a + (-56a + 7a2)) + (14a + -16)(a + -8) = 0 Combine like terms: 9a + -56a = -47a (-72 + -47a + 7a2) + (14a + -16)(a + -8) = 0 Reorder the terms: -72 + -47a + 7a2 + (-16 + 14a)(a + -8) = 0 Reorder the terms: -72 + -47a + 7a2 + (-16 + 14a)(-8 + a) = 0 Multiply (-16 + 14a) * (-8 + a) -72 + -47a + 7a2 + (-16(-8 + a) + 14a * (-8 + a)) = 0 -72 + -47a + 7a2 + ((-8 * -16 + a * -16) + 14a * (-8 + a)) = 0 -72 + -47a + 7a2 + ((128 + -16a) + 14a * (-8 + a)) = 0 -72 + -47a + 7a2 + (128 + -16a + (-8 * 14a + a * 14a)) = 0 -72 + -47a + 7a2 + (128 + -16a + (-112a + 14a2)) = 0 Combine like terms: -16a + -112a = -128a -72 + -47a + 7a2 + (128 + -128a + 14a2) = 0 Reorder the terms: -72 + 128 + -47a + -128a + 7a2 + 14a2 = 0 Combine like terms: -72 + 128 = 56 56 + -47a + -128a + 7a2 + 14a2 = 0 Combine like terms: -47a + -128a = -175a 56 + -175a + 7a2 + 14a2 = 0 Combine like terms: 7a2 + 14a2 = 21a2 56 + -175a + 21a2 = 0 Solving 56 + -175a + 21a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7'. 7(8 + -25a + 3a2) = 0 Factor a trinomial. 7((1 + -3a)(8 + -1a)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 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 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve: Simplifying 8 + -1a = 0 Solving 8 + -1a = 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 + -1a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a = 0 + -8 -1a = 0 + -8 Combine like terms: 0 + -8 = -8 -1a = -8 Divide each side by '-1'. a = 8 Simplifying a = 8Solution
a = {0.3333333333, 8}
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