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Simplifying 9(d + -2) * 2d = 14 + 11d Reorder the terms: 9(-2 + d) * 2d = 14 + 11d Reorder the terms for easier multiplication: 9 * 2d(-2 + d) = 14 + 11d Multiply 9 * 2 18d(-2 + d) = 14 + 11d (-2 * 18d + d * 18d) = 14 + 11d (-36d + 18d2) = 14 + 11d Solving -36d + 18d2 = 14 + 11d Solving for variable 'd'. Reorder the terms: -14 + -36d + -11d + 18d2 = 14 + 11d + -14 + -11d Combine like terms: -36d + -11d = -47d -14 + -47d + 18d2 = 14 + 11d + -14 + -11d Reorder the terms: -14 + -47d + 18d2 = 14 + -14 + 11d + -11d Combine like terms: 14 + -14 = 0 -14 + -47d + 18d2 = 0 + 11d + -11d -14 + -47d + 18d2 = 11d + -11d Combine like terms: 11d + -11d = 0 -14 + -47d + 18d2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.7777777778 + -2.611111111d + d2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -2.611111111d + 0.7777777778 + d2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -2.611111111d + d2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -2.611111111d + d2 = 0 + 0.7777777778 -2.611111111d + d2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -2.611111111d + d2 = 0.7777777778 The d term is -2.611111111d. Take half its coefficient (-1.305555556). Square it (1.704475310) and add it to both sides. Add '1.704475310' to each side of the equation. -2.611111111d + 1.704475310 + d2 = 0.7777777778 + 1.704475310 Reorder the terms: 1.704475310 + -2.611111111d + d2 = 0.7777777778 + 1.704475310 Combine like terms: 0.7777777778 + 1.704475310 = 2.4822530878 1.704475310 + -2.611111111d + d2 = 2.4822530878 Factor a perfect square on the left side: (d + -1.305555556)(d + -1.305555556) = 2.4822530878 Calculate the square root of the right side: 1.575516768 Break this problem into two subproblems by setting (d + -1.305555556) equal to 1.575516768 and -1.575516768.Subproblem 1
d + -1.305555556 = 1.575516768 Simplifying d + -1.305555556 = 1.575516768 Reorder the terms: -1.305555556 + d = 1.575516768 Solving -1.305555556 + d = 1.575516768 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.305555556' to each side of the equation. -1.305555556 + 1.305555556 + d = 1.575516768 + 1.305555556 Combine like terms: -1.305555556 + 1.305555556 = 0.000000000 0.000000000 + d = 1.575516768 + 1.305555556 d = 1.575516768 + 1.305555556 Combine like terms: 1.575516768 + 1.305555556 = 2.881072324 d = 2.881072324 Simplifying d = 2.881072324Subproblem 2
d + -1.305555556 = -1.575516768 Simplifying d + -1.305555556 = -1.575516768 Reorder the terms: -1.305555556 + d = -1.575516768 Solving -1.305555556 + d = -1.575516768 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.305555556' to each side of the equation. -1.305555556 + 1.305555556 + d = -1.575516768 + 1.305555556 Combine like terms: -1.305555556 + 1.305555556 = 0.000000000 0.000000000 + d = -1.575516768 + 1.305555556 d = -1.575516768 + 1.305555556 Combine like terms: -1.575516768 + 1.305555556 = -0.269961212 d = -0.269961212 Simplifying d = -0.269961212Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.881072324, -0.269961212}
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