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Simplifying (a + -5)(a + -2) = 28 Reorder the terms: (-5 + a)(a + -2) = 28 Reorder the terms: (-5 + a)(-2 + a) = 28 Multiply (-5 + a) * (-2 + a) (-5(-2 + a) + a(-2 + a)) = 28 ((-2 * -5 + a * -5) + a(-2 + a)) = 28 ((10 + -5a) + a(-2 + a)) = 28 (10 + -5a + (-2 * a + a * a)) = 28 (10 + -5a + (-2a + a2)) = 28 Combine like terms: -5a + -2a = -7a (10 + -7a + a2) = 28 Solving 10 + -7a + a2 = 28 Solving for variable 'a'. Reorder the terms: 10 + -28 + -7a + a2 = 28 + -28 Combine like terms: 10 + -28 = -18 -18 + -7a + a2 = 28 + -28 Combine like terms: 28 + -28 = 0 -18 + -7a + a2 = 0 Factor a trinomial. (-2 + -1a)(9 + -1a) = 0Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2Subproblem 2
Set the factor '(9 + -1a)' equal to zero and attempt to solve: Simplifying 9 + -1a = 0 Solving 9 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1a = 0 + -9 -1a = 0 + -9 Combine like terms: 0 + -9 = -9 -1a = -9 Divide each side by '-1'. a = 9 Simplifying a = 9Solution
a = {-2, 9}
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