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Simplifying 7a2 + -17a = -36 + -5a + 6a2 Reorder the terms: -17a + 7a2 = -36 + -5a + 6a2 Solving -17a + 7a2 = -36 + -5a + 6a2 Solving for variable 'a'. Reorder the terms: 36 + -17a + 5a + 7a2 + -6a2 = -36 + -5a + 6a2 + 36 + 5a + -6a2 Combine like terms: -17a + 5a = -12a 36 + -12a + 7a2 + -6a2 = -36 + -5a + 6a2 + 36 + 5a + -6a2 Combine like terms: 7a2 + -6a2 = 1a2 36 + -12a + 1a2 = -36 + -5a + 6a2 + 36 + 5a + -6a2 Reorder the terms: 36 + -12a + 1a2 = -36 + 36 + -5a + 5a + 6a2 + -6a2 Combine like terms: -36 + 36 = 0 36 + -12a + 1a2 = 0 + -5a + 5a + 6a2 + -6a2 36 + -12a + 1a2 = -5a + 5a + 6a2 + -6a2 Combine like terms: -5a + 5a = 0 36 + -12a + 1a2 = 0 + 6a2 + -6a2 36 + -12a + 1a2 = 6a2 + -6a2 Combine like terms: 6a2 + -6a2 = 0 36 + -12a + 1a2 = 0 Factor a trinomial. (6 + -1a)(6 + -1a) = 0Subproblem 1
Set the factor '(6 + -1a)' equal to zero and attempt to solve: Simplifying 6 + -1a = 0 Solving 6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1a = 0 + -6 -1a = 0 + -6 Combine like terms: 0 + -6 = -6 -1a = -6 Divide each side by '-1'. a = 6 Simplifying a = 6Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve: Simplifying 6 + -1a = 0 Solving 6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1a = 0 + -6 -1a = 0 + -6 Combine like terms: 0 + -6 = -6 -1a = -6 Divide each side by '-1'. a = 6 Simplifying a = 6Solution
a = {6, 6}
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