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Simplifying 21a2 + 13a = 2a + 7a2 + 15 Reorder the terms: 13a + 21a2 = 2a + 7a2 + 15 Reorder the terms: 13a + 21a2 = 15 + 2a + 7a2 Solving 13a + 21a2 = 15 + 2a + 7a2 Solving for variable 'a'. Reorder the terms: -15 + 13a + -2a + 21a2 + -7a2 = 15 + 2a + 7a2 + -15 + -2a + -7a2 Combine like terms: 13a + -2a = 11a -15 + 11a + 21a2 + -7a2 = 15 + 2a + 7a2 + -15 + -2a + -7a2 Combine like terms: 21a2 + -7a2 = 14a2 -15 + 11a + 14a2 = 15 + 2a + 7a2 + -15 + -2a + -7a2 Reorder the terms: -15 + 11a + 14a2 = 15 + -15 + 2a + -2a + 7a2 + -7a2 Combine like terms: 15 + -15 = 0 -15 + 11a + 14a2 = 0 + 2a + -2a + 7a2 + -7a2 -15 + 11a + 14a2 = 2a + -2a + 7a2 + -7a2 Combine like terms: 2a + -2a = 0 -15 + 11a + 14a2 = 0 + 7a2 + -7a2 -15 + 11a + 14a2 = 7a2 + -7a2 Combine like terms: 7a2 + -7a2 = 0 -15 + 11a + 14a2 = 0 Factor a trinomial. (-3 + -2a)(5 + -7a) = 0Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5Subproblem 2
Set the factor '(5 + -7a)' equal to zero and attempt to solve: Simplifying 5 + -7a = 0 Solving 5 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7a = 0 + -5 -7a = 0 + -5 Combine like terms: 0 + -5 = -5 -7a = -5 Divide each side by '-7'. a = 0.7142857143 Simplifying a = 0.7142857143Solution
a = {-1.5, 0.7142857143}
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