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Simplifying 3a2 + 4a + -7 = -3a2 + -7a + 10 Reorder the terms: -7 + 4a + 3a2 = -3a2 + -7a + 10 Reorder the terms: -7 + 4a + 3a2 = 10 + -7a + -3a2 Solving -7 + 4a + 3a2 = 10 + -7a + -3a2 Solving for variable 'a'. Reorder the terms: -7 + -10 + 4a + 7a + 3a2 + 3a2 = 10 + -7a + -3a2 + -10 + 7a + 3a2 Combine like terms: -7 + -10 = -17 -17 + 4a + 7a + 3a2 + 3a2 = 10 + -7a + -3a2 + -10 + 7a + 3a2 Combine like terms: 4a + 7a = 11a -17 + 11a + 3a2 + 3a2 = 10 + -7a + -3a2 + -10 + 7a + 3a2 Combine like terms: 3a2 + 3a2 = 6a2 -17 + 11a + 6a2 = 10 + -7a + -3a2 + -10 + 7a + 3a2 Reorder the terms: -17 + 11a + 6a2 = 10 + -10 + -7a + 7a + -3a2 + 3a2 Combine like terms: 10 + -10 = 0 -17 + 11a + 6a2 = 0 + -7a + 7a + -3a2 + 3a2 -17 + 11a + 6a2 = -7a + 7a + -3a2 + 3a2 Combine like terms: -7a + 7a = 0 -17 + 11a + 6a2 = 0 + -3a2 + 3a2 -17 + 11a + 6a2 = -3a2 + 3a2 Combine like terms: -3a2 + 3a2 = 0 -17 + 11a + 6a2 = 0 Factor a trinomial. (-17 + -6a)(1 + -1a) = 0Subproblem 1
Set the factor '(-17 + -6a)' equal to zero and attempt to solve: Simplifying -17 + -6a = 0 Solving -17 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -6a = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -6a = 0 + 17 -6a = 0 + 17 Combine like terms: 0 + 17 = 17 -6a = 17 Divide each side by '-6'. a = -2.833333333 Simplifying a = -2.833333333Subproblem 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 = {-2.833333333, 1}
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