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Simplifying 26d2 + -84d + 49 = 0 Reorder the terms: 49 + -84d + 26d2 = 0 Solving 49 + -84d + 26d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 1.884615385 + -3.230769231d + d2 = 0 Move the constant term to the right: Add '-1.884615385' to each side of the equation. 1.884615385 + -3.230769231d + -1.884615385 + d2 = 0 + -1.884615385 Reorder the terms: 1.884615385 + -1.884615385 + -3.230769231d + d2 = 0 + -1.884615385 Combine like terms: 1.884615385 + -1.884615385 = 0.000000000 0.000000000 + -3.230769231d + d2 = 0 + -1.884615385 -3.230769231d + d2 = 0 + -1.884615385 Combine like terms: 0 + -1.884615385 = -1.884615385 -3.230769231d + d2 = -1.884615385 The d term is -3.230769231d. Take half its coefficient (-1.615384616). Square it (2.609467458) and add it to both sides. Add '2.609467458' to each side of the equation. -3.230769231d + 2.609467458 + d2 = -1.884615385 + 2.609467458 Reorder the terms: 2.609467458 + -3.230769231d + d2 = -1.884615385 + 2.609467458 Combine like terms: -1.884615385 + 2.609467458 = 0.724852073 2.609467458 + -3.230769231d + d2 = 0.724852073 Factor a perfect square on the left side: (d + -1.615384616)(d + -1.615384616) = 0.724852073 Calculate the square root of the right side: 0.851382448 Break this problem into two subproblems by setting (d + -1.615384616) equal to 0.851382448 and -0.851382448.Subproblem 1
d + -1.615384616 = 0.851382448 Simplifying d + -1.615384616 = 0.851382448 Reorder the terms: -1.615384616 + d = 0.851382448 Solving -1.615384616 + d = 0.851382448 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.615384616' to each side of the equation. -1.615384616 + 1.615384616 + d = 0.851382448 + 1.615384616 Combine like terms: -1.615384616 + 1.615384616 = 0.000000000 0.000000000 + d = 0.851382448 + 1.615384616 d = 0.851382448 + 1.615384616 Combine like terms: 0.851382448 + 1.615384616 = 2.466767064 d = 2.466767064 Simplifying d = 2.466767064Subproblem 2
d + -1.615384616 = -0.851382448 Simplifying d + -1.615384616 = -0.851382448 Reorder the terms: -1.615384616 + d = -0.851382448 Solving -1.615384616 + d = -0.851382448 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.615384616' to each side of the equation. -1.615384616 + 1.615384616 + d = -0.851382448 + 1.615384616 Combine like terms: -1.615384616 + 1.615384616 = 0.000000000 0.000000000 + d = -0.851382448 + 1.615384616 d = -0.851382448 + 1.615384616 Combine like terms: -0.851382448 + 1.615384616 = 0.764002168 d = 0.764002168 Simplifying d = 0.764002168Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.466767064, 0.764002168}
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