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Simplifying (5 + -2a)(1 + -2a) = 0 Multiply (5 + -2a) * (1 + -2a) (5(1 + -2a) + -2a * (1 + -2a)) = 0 ((1 * 5 + -2a * 5) + -2a * (1 + -2a)) = 0 ((5 + -10a) + -2a * (1 + -2a)) = 0 (5 + -10a + (1 * -2a + -2a * -2a)) = 0 (5 + -10a + (-2a + 4a2)) = 0 Combine like terms: -10a + -2a = -12a (5 + -12a + 4a2) = 0 Solving 5 + -12a + 4a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -2a)(5 + -2a) = 0Subproblem 1
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 = 0.5Subproblem 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 = {0.5, 2.5}
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