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Simplifying (2a + -1)(5a + 2) = 0 Reorder the terms: (-1 + 2a)(5a + 2) = 0 Reorder the terms: (-1 + 2a)(2 + 5a) = 0 Multiply (-1 + 2a) * (2 + 5a) (-1(2 + 5a) + 2a * (2 + 5a)) = 0 ((2 * -1 + 5a * -1) + 2a * (2 + 5a)) = 0 ((-2 + -5a) + 2a * (2 + 5a)) = 0 (-2 + -5a + (2 * 2a + 5a * 2a)) = 0 (-2 + -5a + (4a + 10a2)) = 0 Combine like terms: -5a + 4a = -1a (-2 + -1a + 10a2) = 0 Solving -2 + -1a + 10a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -5a)(1 + -2a) = 0Subproblem 1
Set the factor '(-2 + -5a)' equal to zero and attempt to solve: Simplifying -2 + -5a = 0 Solving -2 + -5a = 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 + -5a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5a = 0 + 2 -5a = 0 + 2 Combine like terms: 0 + 2 = 2 -5a = 2 Divide each side by '-5'. a = -0.4 Simplifying a = -0.4Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {-0.4, 0.5}
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