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Simplifying 12a2 = -28 + 40a Solving 12a2 = -28 + 40a Solving for variable 'a'. Reorder the terms: 28 + -40a + 12a2 = -28 + 40a + 28 + -40a Reorder the terms: 28 + -40a + 12a2 = -28 + 28 + 40a + -40a Combine like terms: -28 + 28 = 0 28 + -40a + 12a2 = 0 + 40a + -40a 28 + -40a + 12a2 = 40a + -40a Combine like terms: 40a + -40a = 0 28 + -40a + 12a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -10a + 3a2) = 0 Factor a trinomial. 4((1 + -1a)(7 + -3a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Subproblem 2
Set the factor '(7 + -3a)' equal to zero and attempt to solve: Simplifying 7 + -3a = 0 Solving 7 + -3a = 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 + -3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3a = 0 + -7 -3a = 0 + -7 Combine like terms: 0 + -7 = -7 -3a = -7 Divide each side by '-3'. a = 2.333333333 Simplifying a = 2.333333333Solution
a = {1, 2.333333333}
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