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Simplifying (a + 5)(5a + -1) = 0 Reorder the terms: (5 + a)(5a + -1) = 0 Reorder the terms: (5 + a)(-1 + 5a) = 0 Multiply (5 + a) * (-1 + 5a) (5(-1 + 5a) + a(-1 + 5a)) = 0 ((-1 * 5 + 5a * 5) + a(-1 + 5a)) = 0 ((-5 + 25a) + a(-1 + 5a)) = 0 (-5 + 25a + (-1 * a + 5a * a)) = 0 (-5 + 25a + (-1a + 5a2)) = 0 Combine like terms: 25a + -1a = 24a (-5 + 24a + 5a2) = 0 Solving -5 + 24a + 5a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -1a)(1 + -5a) = 0Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve: Simplifying -5 + -1a = 0 Solving -5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1a = 0 + 5 -1a = 0 + 5 Combine like terms: 0 + 5 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5Subproblem 2
Set the factor '(1 + -5a)' equal to zero and attempt to solve: Simplifying 1 + -5a = 0 Solving 1 + -5a = 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 + -5a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5a = 0 + -1 -5a = 0 + -1 Combine like terms: 0 + -1 = -1 -5a = -1 Divide each side by '-5'. a = 0.2 Simplifying a = 0.2Solution
a = {-5, 0.2}
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