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Simplifying 8.41D2 + -13433.42D + -20977 = 0 Reorder the terms: -20977 + -13433.42D + 8.41D2 = 0 Solving -20977 + -13433.42D + 8.41D2 = 0 Solving for variable 'D'. Begin completing the square. Divide all terms by 8.41 the coefficient of the squared term: Divide each side by '8.41'. -2494.292509 + -1597.315101D + D2 = 0 Move the constant term to the right: Add '2494.292509' to each side of the equation. -2494.292509 + -1597.315101D + 2494.292509 + D2 = 0 + 2494.292509 Reorder the terms: -2494.292509 + 2494.292509 + -1597.315101D + D2 = 0 + 2494.292509 Combine like terms: -2494.292509 + 2494.292509 = 0.000000 0.000000 + -1597.315101D + D2 = 0 + 2494.292509 -1597.315101D + D2 = 0 + 2494.292509 Combine like terms: 0 + 2494.292509 = 2494.292509 -1597.315101D + D2 = 2494.292509 The D term is -1597.315101D. Take half its coefficient (-798.6575505). Square it (637853.8830) and add it to both sides. Add '637853.8830' to each side of the equation. -1597.315101D + 637853.8830 + D2 = 2494.292509 + 637853.8830 Reorder the terms: 637853.8830 + -1597.315101D + D2 = 2494.292509 + 637853.8830 Combine like terms: 2494.292509 + 637853.8830 = 640348.175509 637853.8830 + -1597.315101D + D2 = 640348.175509 Factor a perfect square on the left side: (D + -798.6575505)(D + -798.6575505) = 640348.175509 Calculate the square root of the right side: 800.217580105 Break this problem into two subproblems by setting (D + -798.6575505) equal to 800.217580105 and -800.217580105.Subproblem 1
D + -798.6575505 = 800.217580105 Simplifying D + -798.6575505 = 800.217580105 Reorder the terms: -798.6575505 + D = 800.217580105 Solving -798.6575505 + D = 800.217580105 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '798.6575505' to each side of the equation. -798.6575505 + 798.6575505 + D = 800.217580105 + 798.6575505 Combine like terms: -798.6575505 + 798.6575505 = 0.0000000 0.0000000 + D = 800.217580105 + 798.6575505 D = 800.217580105 + 798.6575505 Combine like terms: 800.217580105 + 798.6575505 = 1598.875130605 D = 1598.875130605 Simplifying D = 1598.875130605Subproblem 2
D + -798.6575505 = -800.217580105 Simplifying D + -798.6575505 = -800.217580105 Reorder the terms: -798.6575505 + D = -800.217580105 Solving -798.6575505 + D = -800.217580105 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '798.6575505' to each side of the equation. -798.6575505 + 798.6575505 + D = -800.217580105 + 798.6575505 Combine like terms: -798.6575505 + 798.6575505 = 0.0000000 0.0000000 + D = -800.217580105 + 798.6575505 D = -800.217580105 + 798.6575505 Combine like terms: -800.217580105 + 798.6575505 = -1.560029605 D = -1.560029605 Simplifying D = -1.560029605Solution
The solution to the problem is based on the solutions from the subproblems. D = {1598.875130605, -1.560029605}
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