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Simplifying 7a2 = 65a + -18 Reorder the terms: 7a2 = -18 + 65a Solving 7a2 = -18 + 65a Solving for variable 'a'. Reorder the terms: 18 + -65a + 7a2 = -18 + 65a + 18 + -65a Reorder the terms: 18 + -65a + 7a2 = -18 + 18 + 65a + -65a Combine like terms: -18 + 18 = 0 18 + -65a + 7a2 = 0 + 65a + -65a 18 + -65a + 7a2 = 65a + -65a Combine like terms: 65a + -65a = 0 18 + -65a + 7a2 = 0 Factor a trinomial. (2 + -7a)(9 + -1a) = 0Subproblem 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 '(9 + -1a)' equal to zero and attempt to solve: Simplifying 9 + -1a = 0 Solving 9 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1a = 0 + -9 -1a = 0 + -9 Combine like terms: 0 + -9 = -9 -1a = -9 Divide each side by '-1'. a = 9 Simplifying a = 9Solution
a = {0.2857142857, 9}
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