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Simplifying (2a + -5)(a + -2) = 0 Reorder the terms: (-5 + 2a)(a + -2) = 0 Reorder the terms: (-5 + 2a)(-2 + a) = 0 Multiply (-5 + 2a) * (-2 + a) (-5(-2 + a) + 2a * (-2 + a)) = 0 ((-2 * -5 + a * -5) + 2a * (-2 + a)) = 0 ((10 + -5a) + 2a * (-2 + a)) = 0 (10 + -5a + (-2 * 2a + a * 2a)) = 0 (10 + -5a + (-4a + 2a2)) = 0 Combine like terms: -5a + -4a = -9a (10 + -9a + 2a2) = 0 Solving 10 + -9a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (2 + -1a)(5 + -2a) = 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 '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 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 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5Solution
a = {2, 2.5}
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