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Simplifying a2 + 18a + -106 = -10 Reorder the terms: -106 + 18a + a2 = -10 Solving -106 + 18a + a2 = -10 Solving for variable 'a'. Reorder the terms: -106 + 10 + 18a + a2 = -10 + 10 Combine like terms: -106 + 10 = -96 -96 + 18a + a2 = -10 + 10 Combine like terms: -10 + 10 = 0 -96 + 18a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 18a + 96 + a2 = 0 + 96 Reorder the terms: -96 + 96 + 18a + a2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 18a + a2 = 0 + 96 18a + a2 = 0 + 96 Combine like terms: 0 + 96 = 96 18a + a2 = 96 The a term is 18a. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18a + 81 + a2 = 96 + 81 Reorder the terms: 81 + 18a + a2 = 96 + 81 Combine like terms: 96 + 81 = 177 81 + 18a + a2 = 177 Factor a perfect square on the left side: (a + 9)(a + 9) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (a + 9) equal to 13.304134696 and -13.304134696.Subproblem 1
a + 9 = 13.304134696 Simplifying a + 9 = 13.304134696 Reorder the terms: 9 + a = 13.304134696 Solving 9 + a = 13.304134696 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = 13.304134696 + -9 Combine like terms: 9 + -9 = 0 0 + a = 13.304134696 + -9 a = 13.304134696 + -9 Combine like terms: 13.304134696 + -9 = 4.304134696 a = 4.304134696 Simplifying a = 4.304134696Subproblem 2
a + 9 = -13.304134696 Simplifying a + 9 = -13.304134696 Reorder the terms: 9 + a = -13.304134696 Solving 9 + a = -13.304134696 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = -13.304134696 + -9 Combine like terms: 9 + -9 = 0 0 + a = -13.304134696 + -9 a = -13.304134696 + -9 Combine like terms: -13.304134696 + -9 = -22.304134696 a = -22.304134696 Simplifying a = -22.304134696Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.304134696, -22.304134696}
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