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Simplifying d2 + -7d + 4 = 0 Reorder the terms: 4 + -7d + d2 = 0 Solving 4 + -7d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7d + -4 + d2 = 0 + -4 Reorder the terms: 4 + -4 + -7d + d2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7d + d2 = 0 + -4 -7d + d2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7d + d2 = -4 The d term is -7d. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7d + 12.25 + d2 = -4 + 12.25 Reorder the terms: 12.25 + -7d + d2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + -7d + d2 = 8.25 Factor a perfect square on the left side: (d + -3.5)(d + -3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (d + -3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
d + -3.5 = 2.872281323 Simplifying d + -3.5 = 2.872281323 Reorder the terms: -3.5 + d = 2.872281323 Solving -3.5 + d = 2.872281323 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + d = 2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + d = 2.872281323 + 3.5 d = 2.872281323 + 3.5 Combine like terms: 2.872281323 + 3.5 = 6.372281323 d = 6.372281323 Simplifying d = 6.372281323Subproblem 2
d + -3.5 = -2.872281323 Simplifying d + -3.5 = -2.872281323 Reorder the terms: -3.5 + d = -2.872281323 Solving -3.5 + d = -2.872281323 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + d = -2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + d = -2.872281323 + 3.5 d = -2.872281323 + 3.5 Combine like terms: -2.872281323 + 3.5 = 0.627718677 d = 0.627718677 Simplifying d = 0.627718677Solution
The solution to the problem is based on the solutions from the subproblems. d = {6.372281323, 0.627718677}
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