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Simplifying a2 + 8a + -11 = 6 Reorder the terms: -11 + 8a + a2 = 6 Solving -11 + 8a + a2 = 6 Solving for variable 'a'. Reorder the terms: -11 + -6 + 8a + a2 = 6 + -6 Combine like terms: -11 + -6 = -17 -17 + 8a + a2 = 6 + -6 Combine like terms: 6 + -6 = 0 -17 + 8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 8a + 17 + a2 = 0 + 17 Reorder the terms: -17 + 17 + 8a + a2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 8a + a2 = 0 + 17 8a + a2 = 0 + 17 Combine like terms: 0 + 17 = 17 8a + a2 = 17 The a term is 8a. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8a + 16 + a2 = 17 + 16 Reorder the terms: 16 + 8a + a2 = 17 + 16 Combine like terms: 17 + 16 = 33 16 + 8a + a2 = 33 Factor a perfect square on the left side: (a + 4)(a + 4) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (a + 4) equal to 5.744562647 and -5.744562647.Subproblem 1
a + 4 = 5.744562647 Simplifying a + 4 = 5.744562647 Reorder the terms: 4 + a = 5.744562647 Solving 4 + a = 5.744562647 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + a = 5.744562647 + -4 a = 5.744562647 + -4 Combine like terms: 5.744562647 + -4 = 1.744562647 a = 1.744562647 Simplifying a = 1.744562647Subproblem 2
a + 4 = -5.744562647 Simplifying a + 4 = -5.744562647 Reorder the terms: 4 + a = -5.744562647 Solving 4 + a = -5.744562647 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = -5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + a = -5.744562647 + -4 a = -5.744562647 + -4 Combine like terms: -5.744562647 + -4 = -9.744562647 a = -9.744562647 Simplifying a = -9.744562647Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.744562647, -9.744562647}
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