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Simplifying d2 + 14d + 28 = 0 Reorder the terms: 28 + 14d + d2 = 0 Solving 28 + 14d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 14d + -28 + d2 = 0 + -28 Reorder the terms: 28 + -28 + 14d + d2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 14d + d2 = 0 + -28 14d + d2 = 0 + -28 Combine like terms: 0 + -28 = -28 14d + d2 = -28 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 = -28 + 49 Reorder the terms: 49 + 14d + d2 = -28 + 49 Combine like terms: -28 + 49 = 21 49 + 14d + d2 = 21 Factor a perfect square on the left side: (d + 7)(d + 7) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (d + 7) equal to 4.582575695 and -4.582575695.Subproblem 1
d + 7 = 4.582575695 Simplifying d + 7 = 4.582575695 Reorder the terms: 7 + d = 4.582575695 Solving 7 + d = 4.582575695 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 = 4.582575695 + -7 Combine like terms: 7 + -7 = 0 0 + d = 4.582575695 + -7 d = 4.582575695 + -7 Combine like terms: 4.582575695 + -7 = -2.417424305 d = -2.417424305 Simplifying d = -2.417424305Subproblem 2
d + 7 = -4.582575695 Simplifying d + 7 = -4.582575695 Reorder the terms: 7 + d = -4.582575695 Solving 7 + d = -4.582575695 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 = -4.582575695 + -7 Combine like terms: 7 + -7 = 0 0 + d = -4.582575695 + -7 d = -4.582575695 + -7 Combine like terms: -4.582575695 + -7 = -11.582575695 d = -11.582575695 Simplifying d = -11.582575695Solution
The solution to the problem is based on the solutions from the subproblems. d = {-2.417424305, -11.582575695}
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