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Simplifying d2 + -28d = 25 Reorder the terms: -28d + d2 = 25 Solving -28d + d2 = 25 Solving for variable 'd'. Reorder the terms: -25 + -28d + d2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -28d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -28d + 25 + d2 = 0 + 25 Reorder the terms: -25 + 25 + -28d + d2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -28d + d2 = 0 + 25 -28d + d2 = 0 + 25 Combine like terms: 0 + 25 = 25 -28d + d2 = 25 The d term is -28d. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28d + 196 + d2 = 25 + 196 Reorder the terms: 196 + -28d + d2 = 25 + 196 Combine like terms: 25 + 196 = 221 196 + -28d + d2 = 221 Factor a perfect square on the left side: (d + -14)(d + -14) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (d + -14) equal to 14.866068747 and -14.866068747.Subproblem 1
d + -14 = 14.866068747 Simplifying d + -14 = 14.866068747 Reorder the terms: -14 + d = 14.866068747 Solving -14 + d = 14.866068747 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + d = 14.866068747 + 14 Combine like terms: -14 + 14 = 0 0 + d = 14.866068747 + 14 d = 14.866068747 + 14 Combine like terms: 14.866068747 + 14 = 28.866068747 d = 28.866068747 Simplifying d = 28.866068747Subproblem 2
d + -14 = -14.866068747 Simplifying d + -14 = -14.866068747 Reorder the terms: -14 + d = -14.866068747 Solving -14 + d = -14.866068747 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + d = -14.866068747 + 14 Combine like terms: -14 + 14 = 0 0 + d = -14.866068747 + 14 d = -14.866068747 + 14 Combine like terms: -14.866068747 + 14 = -0.866068747 d = -0.866068747 Simplifying d = -0.866068747Solution
The solution to the problem is based on the solutions from the subproblems. d = {28.866068747, -0.866068747}
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