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Simplifying d2 + 14d + 13 = 1 Reorder the terms: 13 + 14d + d2 = 1 Solving 13 + 14d + d2 = 1 Solving for variable 'd'. Reorder the terms: 13 + -1 + 14d + d2 = 1 + -1 Combine like terms: 13 + -1 = 12 12 + 14d + d2 = 1 + -1 Combine like terms: 1 + -1 = 0 12 + 14d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 14d + -12 + d2 = 0 + -12 Reorder the terms: 12 + -12 + 14d + d2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 14d + d2 = 0 + -12 14d + d2 = 0 + -12 Combine like terms: 0 + -12 = -12 14d + d2 = -12 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 = -12 + 49 Reorder the terms: 49 + 14d + d2 = -12 + 49 Combine like terms: -12 + 49 = 37 49 + 14d + d2 = 37 Factor a perfect square on the left side: (d + 7)(d + 7) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (d + 7) equal to 6.08276253 and -6.08276253.Subproblem 1
d + 7 = 6.08276253 Simplifying d + 7 = 6.08276253 Reorder the terms: 7 + d = 6.08276253 Solving 7 + d = 6.08276253 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 = 6.08276253 + -7 Combine like terms: 7 + -7 = 0 0 + d = 6.08276253 + -7 d = 6.08276253 + -7 Combine like terms: 6.08276253 + -7 = -0.91723747 d = -0.91723747 Simplifying d = -0.91723747Subproblem 2
d + 7 = -6.08276253 Simplifying d + 7 = -6.08276253 Reorder the terms: 7 + d = -6.08276253 Solving 7 + d = -6.08276253 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 = -6.08276253 + -7 Combine like terms: 7 + -7 = 0 0 + d = -6.08276253 + -7 d = -6.08276253 + -7 Combine like terms: -6.08276253 + -7 = -13.08276253 d = -13.08276253 Simplifying d = -13.08276253Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.91723747, -13.08276253}
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