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Simplifying 0 = 42a2 + 55a + -25 Reorder the terms: 0 = -25 + 55a + 42a2 Solving 0 = -25 + 55a + 42a2 Solving for variable 'a'. Combine like terms: 0 + 25 = 25 25 + -55a + -42a2 = -25 + 55a + 42a2 + 25 + -55a + -42a2 Reorder the terms: 25 + -55a + -42a2 = -25 + 25 + 55a + -55a + 42a2 + -42a2 Combine like terms: -25 + 25 = 0 25 + -55a + -42a2 = 0 + 55a + -55a + 42a2 + -42a2 25 + -55a + -42a2 = 55a + -55a + 42a2 + -42a2 Combine like terms: 55a + -55a = 0 25 + -55a + -42a2 = 0 + 42a2 + -42a2 25 + -55a + -42a2 = 42a2 + -42a2 Combine like terms: 42a2 + -42a2 = 0 25 + -55a + -42a2 = 0 Factor a trinomial. (5 + -14a)(5 + 3a) = 0Subproblem 1
Set the factor '(5 + -14a)' equal to zero and attempt to solve: Simplifying 5 + -14a = 0 Solving 5 + -14a = 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 + -14a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -14a = 0 + -5 -14a = 0 + -5 Combine like terms: 0 + -5 = -5 -14a = -5 Divide each side by '-14'. a = 0.3571428571 Simplifying a = 0.3571428571Subproblem 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 = {0.3571428571, -1.666666667}
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