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Simplifying d2 + -14d + 22 = 0 Reorder the terms: 22 + -14d + d2 = 0 Solving 22 + -14d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -14d + -22 + d2 = 0 + -22 Reorder the terms: 22 + -22 + -14d + d2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -14d + d2 = 0 + -22 -14d + d2 = 0 + -22 Combine like terms: 0 + -22 = -22 -14d + d2 = -22 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 = -22 + 49 Reorder the terms: 49 + -14d + d2 = -22 + 49 Combine like terms: -22 + 49 = 27 49 + -14d + d2 = 27 Factor a perfect square on the left side: (d + -7)(d + -7) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (d + -7) equal to 5.196152423 and -5.196152423.Subproblem 1
d + -7 = 5.196152423 Simplifying d + -7 = 5.196152423 Reorder the terms: -7 + d = 5.196152423 Solving -7 + d = 5.196152423 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 = 5.196152423 + 7 Combine like terms: -7 + 7 = 0 0 + d = 5.196152423 + 7 d = 5.196152423 + 7 Combine like terms: 5.196152423 + 7 = 12.196152423 d = 12.196152423 Simplifying d = 12.196152423Subproblem 2
d + -7 = -5.196152423 Simplifying d + -7 = -5.196152423 Reorder the terms: -7 + d = -5.196152423 Solving -7 + d = -5.196152423 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 = -5.196152423 + 7 Combine like terms: -7 + 7 = 0 0 + d = -5.196152423 + 7 d = -5.196152423 + 7 Combine like terms: -5.196152423 + 7 = 1.803847577 d = 1.803847577 Simplifying d = 1.803847577Solution
The solution to the problem is based on the solutions from the subproblems. d = {12.196152423, 1.803847577}
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