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Simplifying (d2) + -6d = 14 d2 + -6d = 14 Reorder the terms: -6d + d2 = 14 Solving -6d + d2 = 14 Solving for variable 'd'. Reorder the terms: -14 + -6d + d2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -6d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -6d + 14 + d2 = 0 + 14 Reorder the terms: -14 + 14 + -6d + d2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -6d + d2 = 0 + 14 -6d + d2 = 0 + 14 Combine like terms: 0 + 14 = 14 -6d + d2 = 14 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 = 14 + 9 Reorder the terms: 9 + -6d + d2 = 14 + 9 Combine like terms: 14 + 9 = 23 9 + -6d + d2 = 23 Factor a perfect square on the left side: (d + -3)(d + -3) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (d + -3) equal to 4.795831523 and -4.795831523.Subproblem 1
d + -3 = 4.795831523 Simplifying d + -3 = 4.795831523 Reorder the terms: -3 + d = 4.795831523 Solving -3 + d = 4.795831523 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 = 4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + d = 4.795831523 + 3 d = 4.795831523 + 3 Combine like terms: 4.795831523 + 3 = 7.795831523 d = 7.795831523 Simplifying d = 7.795831523Subproblem 2
d + -3 = -4.795831523 Simplifying d + -3 = -4.795831523 Reorder the terms: -3 + d = -4.795831523 Solving -3 + d = -4.795831523 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 = -4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + d = -4.795831523 + 3 d = -4.795831523 + 3 Combine like terms: -4.795831523 + 3 = -1.795831523 d = -1.795831523 Simplifying d = -1.795831523Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.795831523, -1.795831523}
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