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Simplifying d2 + 11d + -8 = 0 Reorder the terms: -8 + 11d + d2 = 0 Solving -8 + 11d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 11d + 8 + d2 = 0 + 8 Reorder the terms: -8 + 8 + 11d + d2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 11d + d2 = 0 + 8 11d + d2 = 0 + 8 Combine like terms: 0 + 8 = 8 11d + d2 = 8 The d term is 11d. 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. 11d + 30.25 + d2 = 8 + 30.25 Reorder the terms: 30.25 + 11d + d2 = 8 + 30.25 Combine like terms: 8 + 30.25 = 38.25 30.25 + 11d + d2 = 38.25 Factor a perfect square on the left side: (d + 5.5)(d + 5.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (d + 5.5) equal to 6.184658438 and -6.184658438.Subproblem 1
d + 5.5 = 6.184658438 Simplifying d + 5.5 = 6.184658438 Reorder the terms: 5.5 + d = 6.184658438 Solving 5.5 + d = 6.184658438 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + d = 6.184658438 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + d = 6.184658438 + -5.5 d = 6.184658438 + -5.5 Combine like terms: 6.184658438 + -5.5 = 0.684658438 d = 0.684658438 Simplifying d = 0.684658438Subproblem 2
d + 5.5 = -6.184658438 Simplifying d + 5.5 = -6.184658438 Reorder the terms: 5.5 + d = -6.184658438 Solving 5.5 + d = -6.184658438 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + d = -6.184658438 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + d = -6.184658438 + -5.5 d = -6.184658438 + -5.5 Combine like terms: -6.184658438 + -5.5 = -11.684658438 d = -11.684658438 Simplifying d = -11.684658438Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.684658438, -11.684658438}
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