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Simplifying 24a2 + 8 = -4a2 + 36a Reorder the terms: 8 + 24a2 = -4a2 + 36a Reorder the terms: 8 + 24a2 = 36a + -4a2 Solving 8 + 24a2 = 36a + -4a2 Solving for variable 'a'. Reorder the terms: 8 + -36a + 24a2 + 4a2 = 36a + -4a2 + -36a + 4a2 Combine like terms: 24a2 + 4a2 = 28a2 8 + -36a + 28a2 = 36a + -4a2 + -36a + 4a2 Reorder the terms: 8 + -36a + 28a2 = 36a + -36a + -4a2 + 4a2 Combine like terms: 36a + -36a = 0 8 + -36a + 28a2 = 0 + -4a2 + 4a2 8 + -36a + 28a2 = -4a2 + 4a2 Combine like terms: -4a2 + 4a2 = 0 8 + -36a + 28a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -9a + 7a2) = 0 Factor a trinomial. 4((2 + -7a)(1 + -1a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -7a)' equal to zero and attempt to solve: Simplifying 2 + -7a = 0 Solving 2 + -7a = 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 + -7a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7a = 0 + -2 -7a = 0 + -2 Combine like terms: 0 + -2 = -2 -7a = -2 Divide each side by '-7'. a = 0.2857142857 Simplifying a = 0.2857142857Subproblem 2
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 = 1Solution
a = {0.2857142857, 1}
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