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Simplifying 9d2 + -3d + -10 = 0 Reorder the terms: -10 + -3d + 9d2 = 0 Solving -10 + -3d + 9d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -0.3333333333d + d2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -0.3333333333d + 1.111111111 + d2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -0.3333333333d + d2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -0.3333333333d + d2 = 0 + 1.111111111 -0.3333333333d + d2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -0.3333333333d + d2 = 1.111111111 The d term is -0.3333333333d. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333d + 0.02777777779 + d2 = 1.111111111 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333d + d2 = 1.111111111 + 0.02777777779 Combine like terms: 1.111111111 + 0.02777777779 = 1.13888888879 0.02777777779 + -0.3333333333d + d2 = 1.13888888879 Factor a perfect square on the left side: (d + -0.1666666667)(d + -0.1666666667) = 1.13888888879 Calculate the square root of the right side: 1.067187373 Break this problem into two subproblems by setting (d + -0.1666666667) equal to 1.067187373 and -1.067187373.Subproblem 1
d + -0.1666666667 = 1.067187373 Simplifying d + -0.1666666667 = 1.067187373 Reorder the terms: -0.1666666667 + d = 1.067187373 Solving -0.1666666667 + d = 1.067187373 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + d = 1.067187373 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + d = 1.067187373 + 0.1666666667 d = 1.067187373 + 0.1666666667 Combine like terms: 1.067187373 + 0.1666666667 = 1.2338540397 d = 1.2338540397 Simplifying d = 1.2338540397Subproblem 2
d + -0.1666666667 = -1.067187373 Simplifying d + -0.1666666667 = -1.067187373 Reorder the terms: -0.1666666667 + d = -1.067187373 Solving -0.1666666667 + d = -1.067187373 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + d = -1.067187373 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + d = -1.067187373 + 0.1666666667 d = -1.067187373 + 0.1666666667 Combine like terms: -1.067187373 + 0.1666666667 = -0.9005207063 d = -0.9005207063 Simplifying d = -0.9005207063Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.2338540397, -0.9005207063}
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