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Simplifying 2d2 + -1d + -26 = 0 Reorder the terms: -26 + -1d + 2d2 = 0 Solving -26 + -1d + 2d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + -0.5d + d2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -0.5d + 13 + d2 = 0 + 13 Reorder the terms: -13 + 13 + -0.5d + d2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -0.5d + d2 = 0 + 13 -0.5d + d2 = 0 + 13 Combine like terms: 0 + 13 = 13 -0.5d + d2 = 13 The d term is -0.5d. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5d + 0.0625 + d2 = 13 + 0.0625 Reorder the terms: 0.0625 + -0.5d + d2 = 13 + 0.0625 Combine like terms: 13 + 0.0625 = 13.0625 0.0625 + -0.5d + d2 = 13.0625 Factor a perfect square on the left side: (d + -0.25)(d + -0.25) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (d + -0.25) equal to 3.614208074 and -3.614208074.Subproblem 1
d + -0.25 = 3.614208074 Simplifying d + -0.25 = 3.614208074 Reorder the terms: -0.25 + d = 3.614208074 Solving -0.25 + d = 3.614208074 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + d = 3.614208074 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + d = 3.614208074 + 0.25 d = 3.614208074 + 0.25 Combine like terms: 3.614208074 + 0.25 = 3.864208074 d = 3.864208074 Simplifying d = 3.864208074Subproblem 2
d + -0.25 = -3.614208074 Simplifying d + -0.25 = -3.614208074 Reorder the terms: -0.25 + d = -3.614208074 Solving -0.25 + d = -3.614208074 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + d = -3.614208074 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + d = -3.614208074 + 0.25 d = -3.614208074 + 0.25 Combine like terms: -3.614208074 + 0.25 = -3.364208074 d = -3.364208074 Simplifying d = -3.364208074Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.864208074, -3.364208074}
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