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Simplifying (2a + -10)(10a + -2) = 0 Reorder the terms: (-10 + 2a)(10a + -2) = 0 Reorder the terms: (-10 + 2a)(-2 + 10a) = 0 Multiply (-10 + 2a) * (-2 + 10a) (-10(-2 + 10a) + 2a * (-2 + 10a)) = 0 ((-2 * -10 + 10a * -10) + 2a * (-2 + 10a)) = 0 ((20 + -100a) + 2a * (-2 + 10a)) = 0 (20 + -100a + (-2 * 2a + 10a * 2a)) = 0 (20 + -100a + (-4a + 20a2)) = 0 Combine like terms: -100a + -4a = -104a (20 + -104a + 20a2) = 0 Solving 20 + -104a + 20a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -26a + 5a2) = 0 Factor a trinomial. 4((1 + -5a)(5 + -1a)) = 0 Ignore the factor 4.Subproblem 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 '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 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 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {0.2, 5}
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