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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. (2 + -3a)(7 + -2a) = 0Subproblem 1
Set the factor '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve: Simplifying 7 + -2a = 0 Solving 7 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2a = 0 + -7 -2a = 0 + -7 Combine like terms: 0 + -7 = -7 -2a = -7 Divide each side by '-2'. a = 3.5 Simplifying a = 3.5Solution
a = {0.6666666667, 3.5}
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