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Simplifying d2 + 14d = 3 Reorder the terms: 14d + d2 = 3 Solving 14d + d2 = 3 Solving for variable 'd'. Reorder the terms: -3 + 14d + d2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 14d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 14d + 3 + d2 = 0 + 3 Reorder the terms: -3 + 3 + 14d + d2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 14d + d2 = 0 + 3 14d + d2 = 0 + 3 Combine like terms: 0 + 3 = 3 14d + d2 = 3 The d term is 14d. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14d + 49 + d2 = 3 + 49 Reorder the terms: 49 + 14d + d2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + 14d + d2 = 52 Factor a perfect square on the left side: (d + 7)(d + 7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (d + 7) equal to 7.211102551 and -7.211102551.Subproblem 1
d + 7 = 7.211102551 Simplifying d + 7 = 7.211102551 Reorder the terms: 7 + d = 7.211102551 Solving 7 + d = 7.211102551 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + d = 7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + d = 7.211102551 + -7 d = 7.211102551 + -7 Combine like terms: 7.211102551 + -7 = 0.211102551 d = 0.211102551 Simplifying d = 0.211102551Subproblem 2
d + 7 = -7.211102551 Simplifying d + 7 = -7.211102551 Reorder the terms: 7 + d = -7.211102551 Solving 7 + d = -7.211102551 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + d = -7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + d = -7.211102551 + -7 d = -7.211102551 + -7 Combine like terms: -7.211102551 + -7 = -14.211102551 d = -14.211102551 Simplifying d = -14.211102551Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.211102551, -14.211102551}
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