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Simplifying 3(a + 2)(a + 2) + 20(a + -1) + -27 = 0 Reorder the terms: 3(2 + a)(a + 2) + 20(a + -1) + -27 = 0 Reorder the terms: 3(2 + a)(2 + a) + 20(a + -1) + -27 = 0 Multiply (2 + a) * (2 + a) 3(2(2 + a) + a(2 + a)) + 20(a + -1) + -27 = 0 3((2 * 2 + a * 2) + a(2 + a)) + 20(a + -1) + -27 = 0 3((4 + 2a) + a(2 + a)) + 20(a + -1) + -27 = 0 3(4 + 2a + (2 * a + a * a)) + 20(a + -1) + -27 = 0 3(4 + 2a + (2a + a2)) + 20(a + -1) + -27 = 0 Combine like terms: 2a + 2a = 4a 3(4 + 4a + a2) + 20(a + -1) + -27 = 0 (4 * 3 + 4a * 3 + a2 * 3) + 20(a + -1) + -27 = 0 (12 + 12a + 3a2) + 20(a + -1) + -27 = 0 Reorder the terms: 12 + 12a + 3a2 + 20(-1 + a) + -27 = 0 12 + 12a + 3a2 + (-1 * 20 + a * 20) + -27 = 0 12 + 12a + 3a2 + (-20 + 20a) + -27 = 0 Reorder the terms: 12 + -20 + -27 + 12a + 20a + 3a2 = 0 Combine like terms: 12 + -20 = -8 -8 + -27 + 12a + 20a + 3a2 = 0 Combine like terms: -8 + -27 = -35 -35 + 12a + 20a + 3a2 = 0 Combine like terms: 12a + 20a = 32a -35 + 32a + 3a2 = 0 Solving -35 + 32a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-35 + -3a)(1 + -1a) = 0Subproblem 1
Set the factor '(-35 + -3a)' equal to zero and attempt to solve: Simplifying -35 + -3a = 0 Solving -35 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + -3a = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -3a = 0 + 35 -3a = 0 + 35 Combine like terms: 0 + 35 = 35 -3a = 35 Divide each side by '-3'. a = -11.66666667 Simplifying a = -11.66666667Subproblem 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 = {-11.66666667, 1}
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