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Simplifying d2 + 2d + -136 = 0 Reorder the terms: -136 + 2d + d2 = 0 Solving -136 + 2d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + 2d + 136 + d2 = 0 + 136 Reorder the terms: -136 + 136 + 2d + d2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + 2d + d2 = 0 + 136 2d + d2 = 0 + 136 Combine like terms: 0 + 136 = 136 2d + d2 = 136 The d term is 2d. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2d + 1 + d2 = 136 + 1 Reorder the terms: 1 + 2d + d2 = 136 + 1 Combine like terms: 136 + 1 = 137 1 + 2d + d2 = 137 Factor a perfect square on the left side: (d + 1)(d + 1) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (d + 1) equal to 11.704699911 and -11.704699911.Subproblem 1
d + 1 = 11.704699911 Simplifying d + 1 = 11.704699911 Reorder the terms: 1 + d = 11.704699911 Solving 1 + d = 11.704699911 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = 11.704699911 + -1 Combine like terms: 1 + -1 = 0 0 + d = 11.704699911 + -1 d = 11.704699911 + -1 Combine like terms: 11.704699911 + -1 = 10.704699911 d = 10.704699911 Simplifying d = 10.704699911Subproblem 2
d + 1 = -11.704699911 Simplifying d + 1 = -11.704699911 Reorder the terms: 1 + d = -11.704699911 Solving 1 + d = -11.704699911 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = -11.704699911 + -1 Combine like terms: 1 + -1 = 0 0 + d = -11.704699911 + -1 d = -11.704699911 + -1 Combine like terms: -11.704699911 + -1 = -12.704699911 d = -12.704699911 Simplifying d = -12.704699911Solution
The solution to the problem is based on the solutions from the subproblems. d = {10.704699911, -12.704699911}
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