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Simplifying a2 + -11a + -8 = 0 Reorder the terms: -8 + -11a + a2 = 0 Solving -8 + -11a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -11a + 8 + a2 = 0 + 8 Reorder the terms: -8 + 8 + -11a + a2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -11a + a2 = 0 + 8 -11a + a2 = 0 + 8 Combine like terms: 0 + 8 = 8 -11a + a2 = 8 The a term is -11a. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11a + 30.25 + a2 = 8 + 30.25 Reorder the terms: 30.25 + -11a + a2 = 8 + 30.25 Combine like terms: 8 + 30.25 = 38.25 30.25 + -11a + a2 = 38.25 Factor a perfect square on the left side: (a + -5.5)(a + -5.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (a + -5.5) equal to 6.184658438 and -6.184658438.Subproblem 1
a + -5.5 = 6.184658438 Simplifying a + -5.5 = 6.184658438 Reorder the terms: -5.5 + a = 6.184658438 Solving -5.5 + a = 6.184658438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = 6.184658438 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 6.184658438 + 5.5 a = 6.184658438 + 5.5 Combine like terms: 6.184658438 + 5.5 = 11.684658438 a = 11.684658438 Simplifying a = 11.684658438Subproblem 2
a + -5.5 = -6.184658438 Simplifying a + -5.5 = -6.184658438 Reorder the terms: -5.5 + a = -6.184658438 Solving -5.5 + a = -6.184658438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = -6.184658438 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -6.184658438 + 5.5 a = -6.184658438 + 5.5 Combine like terms: -6.184658438 + 5.5 = -0.684658438 a = -0.684658438 Simplifying a = -0.684658438Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.684658438, -0.684658438}
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