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Simplifying 0 = a2 + 17a + 70 Reorder the terms: 0 = 70 + 17a + a2 Solving 0 = 70 + 17a + a2 Solving for variable 'a'. Combine like terms: 0 + -70 = -70 -70 + -17a + -1a2 = 70 + 17a + a2 + -70 + -17a + -1a2 Reorder the terms: -70 + -17a + -1a2 = 70 + -70 + 17a + -17a + a2 + -1a2 Combine like terms: 70 + -70 = 0 -70 + -17a + -1a2 = 0 + 17a + -17a + a2 + -1a2 -70 + -17a + -1a2 = 17a + -17a + a2 + -1a2 Combine like terms: 17a + -17a = 0 -70 + -17a + -1a2 = 0 + a2 + -1a2 -70 + -17a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -70 + -17a + -1a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(70 + 17a + a2) = 0 Factor a trinomial. -1((10 + a)(7 + a)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + a)' equal to zero and attempt to solve: Simplifying 10 + a = 0 Solving 10 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + a = 0 + -10 a = 0 + -10 Combine like terms: 0 + -10 = -10 a = -10 Simplifying a = -10Subproblem 2
Set the factor '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 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 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Solution
a = {-10, -7}
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