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Simplifying 4a + 4 + -3a + 9 = a * a + -8a + 27 Reorder the terms: 4 + 9 + 4a + -3a = a * a + -8a + 27 Combine like terms: 4 + 9 = 13 13 + 4a + -3a = a * a + -8a + 27 Combine like terms: 4a + -3a = 1a 13 + 1a = a * a + -8a + 27 Multiply a * a 13 + 1a = a2 + -8a + 27 Reorder the terms: 13 + 1a = 27 + -8a + a2 Solving 13 + 1a = 27 + -8a + a2 Solving for variable 'a'. Reorder the terms: 13 + -27 + 1a + 8a + -1a2 = 27 + -8a + a2 + -27 + 8a + -1a2 Combine like terms: 13 + -27 = -14 -14 + 1a + 8a + -1a2 = 27 + -8a + a2 + -27 + 8a + -1a2 Combine like terms: 1a + 8a = 9a -14 + 9a + -1a2 = 27 + -8a + a2 + -27 + 8a + -1a2 Reorder the terms: -14 + 9a + -1a2 = 27 + -27 + -8a + 8a + a2 + -1a2 Combine like terms: 27 + -27 = 0 -14 + 9a + -1a2 = 0 + -8a + 8a + a2 + -1a2 -14 + 9a + -1a2 = -8a + 8a + a2 + -1a2 Combine like terms: -8a + 8a = 0 -14 + 9a + -1a2 = 0 + a2 + -1a2 -14 + 9a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -14 + 9a + -1a2 = 0 Factor a trinomial. (-7 + a)(2 + -1a) = 0Subproblem 1
Set the factor '(-7 + a)' equal to zero and attempt to solve: Simplifying -7 + a = 0 Solving -7 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + a = 0 + 7 a = 0 + 7 Combine like terms: 0 + 7 = 7 a = 7 Simplifying a = 7Subproblem 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 = {7, 2}
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