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Simplifying 0 = -6a2 + -25a + -25 Reorder the terms: 0 = -25 + -25a + -6a2 Solving 0 = -25 + -25a + -6a2 Solving for variable 'a'. Combine like terms: 0 + 25 = 25 25 + 25a + 6a2 = -25 + -25a + -6a2 + 25 + 25a + 6a2 Reorder the terms: 25 + 25a + 6a2 = -25 + 25 + -25a + 25a + -6a2 + 6a2 Combine like terms: -25 + 25 = 0 25 + 25a + 6a2 = 0 + -25a + 25a + -6a2 + 6a2 25 + 25a + 6a2 = -25a + 25a + -6a2 + 6a2 Combine like terms: -25a + 25a = 0 25 + 25a + 6a2 = 0 + -6a2 + 6a2 25 + 25a + 6a2 = -6a2 + 6a2 Combine like terms: -6a2 + 6a2 = 0 25 + 25a + 6a2 = 0 Factor a trinomial. (5 + 2a)(5 + 3a) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(5 + 3a)' equal to zero and attempt to solve: Simplifying 5 + 3a = 0 Solving 5 + 3a = 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 + 3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3a = 0 + -5 3a = 0 + -5 Combine like terms: 0 + -5 = -5 3a = -5 Divide each side by '3'. a = -1.666666667 Simplifying a = -1.666666667Solution
a = {-2.5, -1.666666667}
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