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Simplifying d2 + -14d = 5 Reorder the terms: -14d + d2 = 5 Solving -14d + d2 = 5 Solving for variable 'd'. Reorder the terms: -5 + -14d + d2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -14d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -14d + 5 + d2 = 0 + 5 Reorder the terms: -5 + 5 + -14d + d2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -14d + d2 = 0 + 5 -14d + d2 = 0 + 5 Combine like terms: 0 + 5 = 5 -14d + d2 = 5 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 = 5 + 49 Reorder the terms: 49 + -14d + d2 = 5 + 49 Combine like terms: 5 + 49 = 54 49 + -14d + d2 = 54 Factor a perfect square on the left side: (d + -7)(d + -7) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (d + -7) equal to 7.348469228 and -7.348469228.Subproblem 1
d + -7 = 7.348469228 Simplifying d + -7 = 7.348469228 Reorder the terms: -7 + d = 7.348469228 Solving -7 + d = 7.348469228 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 = 7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + d = 7.348469228 + 7 d = 7.348469228 + 7 Combine like terms: 7.348469228 + 7 = 14.348469228 d = 14.348469228 Simplifying d = 14.348469228Subproblem 2
d + -7 = -7.348469228 Simplifying d + -7 = -7.348469228 Reorder the terms: -7 + d = -7.348469228 Solving -7 + d = -7.348469228 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 = -7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + d = -7.348469228 + 7 d = -7.348469228 + 7 Combine like terms: -7.348469228 + 7 = -0.348469228 d = -0.348469228 Simplifying d = -0.348469228Solution
The solution to the problem is based on the solutions from the subproblems. d = {14.348469228, -0.348469228}
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