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Simplifying 4d2 + -8 = d Reorder the terms: -8 + 4d2 = d Solving -8 + 4d2 = d Solving for variable 'd'. Reorder the terms: -8 + -1d + 4d2 = d + -1d Combine like terms: d + -1d = 0 -8 + -1d + 4d2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -0.25d + d2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.25d + 2 + d2 = 0 + 2 Reorder the terms: -2 + 2 + -0.25d + d2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.25d + d2 = 0 + 2 -0.25d + d2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.25d + d2 = 2 The d term is -0.25d. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25d + 0.015625 + d2 = 2 + 0.015625 Reorder the terms: 0.015625 + -0.25d + d2 = 2 + 0.015625 Combine like terms: 2 + 0.015625 = 2.015625 0.015625 + -0.25d + d2 = 2.015625 Factor a perfect square on the left side: (d + -0.125)(d + -0.125) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (d + -0.125) equal to 1.419727086 and -1.419727086.Subproblem 1
d + -0.125 = 1.419727086 Simplifying d + -0.125 = 1.419727086 Reorder the terms: -0.125 + d = 1.419727086 Solving -0.125 + d = 1.419727086 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + d = 1.419727086 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + d = 1.419727086 + 0.125 d = 1.419727086 + 0.125 Combine like terms: 1.419727086 + 0.125 = 1.544727086 d = 1.544727086 Simplifying d = 1.544727086Subproblem 2
d + -0.125 = -1.419727086 Simplifying d + -0.125 = -1.419727086 Reorder the terms: -0.125 + d = -1.419727086 Solving -0.125 + d = -1.419727086 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + d = -1.419727086 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + d = -1.419727086 + 0.125 d = -1.419727086 + 0.125 Combine like terms: -1.419727086 + 0.125 = -1.294727086 d = -1.294727086 Simplifying d = -1.294727086Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.544727086, -1.294727086}
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