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Simplifying 12a2 = 32 + 40a Solving 12a2 = 32 + 40a Solving for variable 'a'. Reorder the terms: -32 + -40a + 12a2 = 32 + 40a + -32 + -40a Reorder the terms: -32 + -40a + 12a2 = 32 + -32 + 40a + -40a Combine like terms: 32 + -32 = 0 -32 + -40a + 12a2 = 0 + 40a + -40a -32 + -40a + 12a2 = 40a + -40a Combine like terms: 40a + -40a = 0 -32 + -40a + 12a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + -10a + 3a2) = 0 Factor a trinomial. 4((-2 + -3a)(4 + -1a)) = 0 Ignore the factor 4.Subproblem 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 '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Solution
a = {-0.6666666667, 4}
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