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Simplifying 0 = -0.005d2 + 0.49d + 1 Reorder the terms: 0 = 1 + 0.49d + -0.005d2 Solving 0 = 1 + 0.49d + -0.005d2 Solving for variable 'd'. Combine like terms: 0 + -1 = -1 -1 + -0.49d + 0.005d2 = 1 + 0.49d + -0.005d2 + -1 + -0.49d + 0.005d2 Reorder the terms: -1 + -0.49d + 0.005d2 = 1 + -1 + 0.49d + -0.49d + -0.005d2 + 0.005d2 Combine like terms: 1 + -1 = 0 -1 + -0.49d + 0.005d2 = 0 + 0.49d + -0.49d + -0.005d2 + 0.005d2 -1 + -0.49d + 0.005d2 = 0.49d + -0.49d + -0.005d2 + 0.005d2 Combine like terms: 0.49d + -0.49d = 0.00 -1 + -0.49d + 0.005d2 = 0.00 + -0.005d2 + 0.005d2 -1 + -0.49d + 0.005d2 = -0.005d2 + 0.005d2 Combine like terms: -0.005d2 + 0.005d2 = 0.000 -1 + -0.49d + 0.005d2 = 0.000 Begin completing the square. Divide all terms by 0.005 the coefficient of the squared term: Divide each side by '0.005'. -200 + -98d + d2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -98d + 200 + d2 = 0 + 200 Reorder the terms: -200 + 200 + -98d + d2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -98d + d2 = 0 + 200 -98d + d2 = 0 + 200 Combine like terms: 0 + 200 = 200 -98d + d2 = 200 The d term is -98d. Take half its coefficient (-49). Square it (2401) and add it to both sides. Add '2401' to each side of the equation. -98d + 2401 + d2 = 200 + 2401 Reorder the terms: 2401 + -98d + d2 = 200 + 2401 Combine like terms: 200 + 2401 = 2601 2401 + -98d + d2 = 2601 Factor a perfect square on the left side: (d + -49)(d + -49) = 2601 Calculate the square root of the right side: 51 Break this problem into two subproblems by setting (d + -49) equal to 51 and -51.Subproblem 1
d + -49 = 51 Simplifying d + -49 = 51 Reorder the terms: -49 + d = 51 Solving -49 + d = 51 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + d = 51 + 49 Combine like terms: -49 + 49 = 0 0 + d = 51 + 49 d = 51 + 49 Combine like terms: 51 + 49 = 100 d = 100 Simplifying d = 100Subproblem 2
d + -49 = -51 Simplifying d + -49 = -51 Reorder the terms: -49 + d = -51 Solving -49 + d = -51 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + d = -51 + 49 Combine like terms: -49 + 49 = 0 0 + d = -51 + 49 d = -51 + 49 Combine like terms: -51 + 49 = -2 d = -2 Simplifying d = -2Solution
The solution to the problem is based on the solutions from the subproblems. d = {100, -2}
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