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Simplifying d2 + 7d = 10 Reorder the terms: 7d + d2 = 10 Solving 7d + d2 = 10 Solving for variable 'd'. Reorder the terms: -10 + 7d + d2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 7d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 7d + 10 + d2 = 0 + 10 Reorder the terms: -10 + 10 + 7d + d2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7d + d2 = 0 + 10 7d + d2 = 0 + 10 Combine like terms: 0 + 10 = 10 7d + d2 = 10 The d term is 7d. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7d + 12.25 + d2 = 10 + 12.25 Reorder the terms: 12.25 + 7d + d2 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + 7d + d2 = 22.25 Factor a perfect square on the left side: (d + 3.5)(d + 3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (d + 3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
d + 3.5 = 4.716990566 Simplifying d + 3.5 = 4.716990566 Reorder the terms: 3.5 + d = 4.716990566 Solving 3.5 + d = 4.716990566 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = 4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = 4.716990566 + -3.5 d = 4.716990566 + -3.5 Combine like terms: 4.716990566 + -3.5 = 1.216990566 d = 1.216990566 Simplifying d = 1.216990566Subproblem 2
d + 3.5 = -4.716990566 Simplifying d + 3.5 = -4.716990566 Reorder the terms: 3.5 + d = -4.716990566 Solving 3.5 + d = -4.716990566 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = -4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = -4.716990566 + -3.5 d = -4.716990566 + -3.5 Combine like terms: -4.716990566 + -3.5 = -8.216990566 d = -8.216990566 Simplifying d = -8.216990566Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.216990566, -8.216990566}
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