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Simplifying (-2a + -1)(5a + -1) = 0 Reorder the terms: (-1 + -2a)(5a + -1) = 0 Reorder the terms: (-1 + -2a)(-1 + 5a) = 0 Multiply (-1 + -2a) * (-1 + 5a) (-1(-1 + 5a) + -2a * (-1 + 5a)) = 0 ((-1 * -1 + 5a * -1) + -2a * (-1 + 5a)) = 0 ((1 + -5a) + -2a * (-1 + 5a)) = 0 (1 + -5a + (-1 * -2a + 5a * -2a)) = 0 (1 + -5a + (2a + -10a2)) = 0 Combine like terms: -5a + 2a = -3a (1 + -3a + -10a2) = 0 Solving 1 + -3a + -10a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -5a)(1 + 2a) = 0Subproblem 1
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 = 0.2Subproblem 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 = {0.2, -0.5}
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