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Simplifying 6a2 = -25a + 14 Reorder the terms: 6a2 = 14 + -25a Solving 6a2 = 14 + -25a Solving for variable 'a'. Reorder the terms: -14 + 25a + 6a2 = 14 + -25a + -14 + 25a Reorder the terms: -14 + 25a + 6a2 = 14 + -14 + -25a + 25a Combine like terms: 14 + -14 = 0 -14 + 25a + 6a2 = 0 + -25a + 25a -14 + 25a + 6a2 = -25a + 25a Combine like terms: -25a + 25a = 0 -14 + 25a + 6a2 = 0 Factor a trinomial. (-14 + -3a)(1 + -2a) = 0Subproblem 1
Set the factor '(-14 + -3a)' equal to zero and attempt to solve: Simplifying -14 + -3a = 0 Solving -14 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -3a = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -3a = 0 + 14 -3a = 0 + 14 Combine like terms: 0 + 14 = 14 -3a = 14 Divide each side by '-3'. a = -4.666666667 Simplifying a = -4.666666667Subproblem 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 = {-4.666666667, 0.5}
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