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Simplifying 43a2 + -72a + 10 = 8a2 + 3a Reorder the terms: 10 + -72a + 43a2 = 8a2 + 3a Reorder the terms: 10 + -72a + 43a2 = 3a + 8a2 Solving 10 + -72a + 43a2 = 3a + 8a2 Solving for variable 'a'. Reorder the terms: 10 + -72a + -3a + 43a2 + -8a2 = 3a + 8a2 + -3a + -8a2 Combine like terms: -72a + -3a = -75a 10 + -75a + 43a2 + -8a2 = 3a + 8a2 + -3a + -8a2 Combine like terms: 43a2 + -8a2 = 35a2 10 + -75a + 35a2 = 3a + 8a2 + -3a + -8a2 Reorder the terms: 10 + -75a + 35a2 = 3a + -3a + 8a2 + -8a2 Combine like terms: 3a + -3a = 0 10 + -75a + 35a2 = 0 + 8a2 + -8a2 10 + -75a + 35a2 = 8a2 + -8a2 Combine like terms: 8a2 + -8a2 = 0 10 + -75a + 35a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -15a + 7a2) = 0 Factor a trinomial. 5((1 + -7a)(2 + -1a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -7a)' equal to zero and attempt to solve: Simplifying 1 + -7a = 0 Solving 1 + -7a = 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 + -7a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7a = 0 + -1 -7a = 0 + -1 Combine like terms: 0 + -1 = -1 -7a = -1 Divide each side by '-7'. a = 0.1428571429 Simplifying a = 0.1428571429Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {0.1428571429, 2}
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