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Simplifying d2 + -6d + 7 = 0 Reorder the terms: 7 + -6d + d2 = 0 Solving 7 + -6d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6d + -7 + d2 = 0 + -7 Reorder the terms: 7 + -7 + -6d + d2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6d + d2 = 0 + -7 -6d + d2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6d + d2 = -7 The d term is -6d. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6d + 9 + d2 = -7 + 9 Reorder the terms: 9 + -6d + d2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6d + d2 = 2 Factor a perfect square on the left side: (d + -3)(d + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (d + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
d + -3 = 1.414213562 Simplifying d + -3 = 1.414213562 Reorder the terms: -3 + d = 1.414213562 Solving -3 + d = 1.414213562 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + d = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + d = 1.414213562 + 3 d = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 d = 4.414213562 Simplifying d = 4.414213562Subproblem 2
d + -3 = -1.414213562 Simplifying d + -3 = -1.414213562 Reorder the terms: -3 + d = -1.414213562 Solving -3 + d = -1.414213562 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + d = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + d = -1.414213562 + 3 d = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 d = 1.585786438 Simplifying d = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.414213562, 1.585786438}
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