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Simplifying (a + 7)(7a + 1) = 0 Reorder the terms: (7 + a)(7a + 1) = 0 Reorder the terms: (7 + a)(1 + 7a) = 0 Multiply (7 + a) * (1 + 7a) (7(1 + 7a) + a(1 + 7a)) = 0 ((1 * 7 + 7a * 7) + a(1 + 7a)) = 0 ((7 + 49a) + a(1 + 7a)) = 0 (7 + 49a + (1 * a + 7a * a)) = 0 (7 + 49a + (1a + 7a2)) = 0 Combine like terms: 49a + 1a = 50a (7 + 50a + 7a2) = 0 Solving 7 + 50a + 7a2 = 0 Solving for variable 'a'. Factor a trinomial. (7 + a)(1 + 7a) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(1 + 7a)' equal to zero and attempt to solve: Simplifying 1 + 7a = 0 Solving 1 + 7a = 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 + 7a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7a = 0 + -1 7a = 0 + -1 Combine like terms: 0 + -1 = -1 7a = -1 Divide each side by '7'. a = -0.1428571429 Simplifying a = -0.1428571429Solution
a = {-7, -0.1428571429}
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