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Simplifying 7d2 = -100d + 4 Reorder the terms: 7d2 = 4 + -100d Solving 7d2 = 4 + -100d Solving for variable 'd'. Reorder the terms: -4 + 100d + 7d2 = 4 + -100d + -4 + 100d Reorder the terms: -4 + 100d + 7d2 = 4 + -4 + -100d + 100d Combine like terms: 4 + -4 = 0 -4 + 100d + 7d2 = 0 + -100d + 100d -4 + 100d + 7d2 = -100d + 100d Combine like terms: -100d + 100d = 0 -4 + 100d + 7d2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 14.28571429d + d2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 14.28571429d + 0.5714285714 + d2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 14.28571429d + d2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 14.28571429d + d2 = 0 + 0.5714285714 14.28571429d + d2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 14.28571429d + d2 = 0.5714285714 The d term is 14.28571429d. Take half its coefficient (7.142857145). Square it (51.02040819) and add it to both sides. Add '51.02040819' to each side of the equation. 14.28571429d + 51.02040819 + d2 = 0.5714285714 + 51.02040819 Reorder the terms: 51.02040819 + 14.28571429d + d2 = 0.5714285714 + 51.02040819 Combine like terms: 0.5714285714 + 51.02040819 = 51.5918367614 51.02040819 + 14.28571429d + d2 = 51.5918367614 Factor a perfect square on the left side: (d + 7.142857145)(d + 7.142857145) = 51.5918367614 Calculate the square root of the right side: 7.182745768 Break this problem into two subproblems by setting (d + 7.142857145) equal to 7.182745768 and -7.182745768.Subproblem 1
d + 7.142857145 = 7.182745768 Simplifying d + 7.142857145 = 7.182745768 Reorder the terms: 7.142857145 + d = 7.182745768 Solving 7.142857145 + d = 7.182745768 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + d = 7.182745768 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + d = 7.182745768 + -7.142857145 d = 7.182745768 + -7.142857145 Combine like terms: 7.182745768 + -7.142857145 = 0.039888623 d = 0.039888623 Simplifying d = 0.039888623Subproblem 2
d + 7.142857145 = -7.182745768 Simplifying d + 7.142857145 = -7.182745768 Reorder the terms: 7.142857145 + d = -7.182745768 Solving 7.142857145 + d = -7.182745768 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + d = -7.182745768 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + d = -7.182745768 + -7.142857145 d = -7.182745768 + -7.142857145 Combine like terms: -7.182745768 + -7.142857145 = -14.325602913 d = -14.325602913 Simplifying d = -14.325602913Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.039888623, -14.325602913}
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