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Simplifying 12a2 = 35 + 16a Solving 12a2 = 35 + 16a Solving for variable 'a'. Reorder the terms: -35 + -16a + 12a2 = 35 + 16a + -35 + -16a Reorder the terms: -35 + -16a + 12a2 = 35 + -35 + 16a + -16a Combine like terms: 35 + -35 = 0 -35 + -16a + 12a2 = 0 + 16a + -16a -35 + -16a + 12a2 = 16a + -16a Combine like terms: 16a + -16a = 0 -35 + -16a + 12a2 = 0 Factor a trinomial. (-7 + -6a)(5 + -2a) = 0Subproblem 1
Set the factor '(-7 + -6a)' equal to zero and attempt to solve: Simplifying -7 + -6a = 0 Solving -7 + -6a = 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 + -6a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6a = 0 + 7 -6a = 0 + 7 Combine like terms: 0 + 7 = 7 -6a = 7 Divide each side by '-6'. a = -1.166666667 Simplifying a = -1.166666667Subproblem 2
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 = 2.5Solution
a = {-1.166666667, 2.5}
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