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Simplifying d2 + -4d + -4 = d + 6 Reorder the terms: -4 + -4d + d2 = d + 6 Reorder the terms: -4 + -4d + d2 = 6 + d Solving -4 + -4d + d2 = 6 + d Solving for variable 'd'. Reorder the terms: -4 + -6 + -4d + -1d + d2 = 6 + d + -6 + -1d Combine like terms: -4 + -6 = -10 -10 + -4d + -1d + d2 = 6 + d + -6 + -1d Combine like terms: -4d + -1d = -5d -10 + -5d + d2 = 6 + d + -6 + -1d Reorder the terms: -10 + -5d + d2 = 6 + -6 + d + -1d Combine like terms: 6 + -6 = 0 -10 + -5d + d2 = 0 + d + -1d -10 + -5d + d2 = d + -1d Combine like terms: d + -1d = 0 -10 + -5d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -5d + 10 + d2 = 0 + 10 Reorder the terms: -10 + 10 + -5d + d2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5d + d2 = 0 + 10 -5d + d2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5d + d2 = 10 The d term is -5d. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5d + 6.25 + d2 = 10 + 6.25 Reorder the terms: 6.25 + -5d + d2 = 10 + 6.25 Combine like terms: 10 + 6.25 = 16.25 6.25 + -5d + d2 = 16.25 Factor a perfect square on the left side: (d + -2.5)(d + -2.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (d + -2.5) equal to 4.031128874 and -4.031128874.Subproblem 1
d + -2.5 = 4.031128874 Simplifying d + -2.5 = 4.031128874 Reorder the terms: -2.5 + d = 4.031128874 Solving -2.5 + d = 4.031128874 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = 4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = 4.031128874 + 2.5 d = 4.031128874 + 2.5 Combine like terms: 4.031128874 + 2.5 = 6.531128874 d = 6.531128874 Simplifying d = 6.531128874Subproblem 2
d + -2.5 = -4.031128874 Simplifying d + -2.5 = -4.031128874 Reorder the terms: -2.5 + d = -4.031128874 Solving -2.5 + d = -4.031128874 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = -4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = -4.031128874 + 2.5 d = -4.031128874 + 2.5 Combine like terms: -4.031128874 + 2.5 = -1.531128874 d = -1.531128874 Simplifying d = -1.531128874Solution
The solution to the problem is based on the solutions from the subproblems. d = {6.531128874, -1.531128874}
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