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Simplifying 11d * 9d + -2 = 5d + 28 Reorder the terms for easier multiplication: 11 * 9d * d + -2 = 5d + 28 Multiply 11 * 9 99d * d + -2 = 5d + 28 Multiply d * d 99d2 + -2 = 5d + 28 Reorder the terms: -2 + 99d2 = 5d + 28 Reorder the terms: -2 + 99d2 = 28 + 5d Solving -2 + 99d2 = 28 + 5d Solving for variable 'd'. Reorder the terms: -2 + -28 + -5d + 99d2 = 28 + 5d + -28 + -5d Combine like terms: -2 + -28 = -30 -30 + -5d + 99d2 = 28 + 5d + -28 + -5d Reorder the terms: -30 + -5d + 99d2 = 28 + -28 + 5d + -5d Combine like terms: 28 + -28 = 0 -30 + -5d + 99d2 = 0 + 5d + -5d -30 + -5d + 99d2 = 5d + -5d Combine like terms: 5d + -5d = 0 -30 + -5d + 99d2 = 0 Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. -0.303030303 + -0.05050505051d + d2 = 0 Move the constant term to the right: Add '0.303030303' to each side of the equation. -0.303030303 + -0.05050505051d + 0.303030303 + d2 = 0 + 0.303030303 Reorder the terms: -0.303030303 + 0.303030303 + -0.05050505051d + d2 = 0 + 0.303030303 Combine like terms: -0.303030303 + 0.303030303 = 0.000000000 0.000000000 + -0.05050505051d + d2 = 0 + 0.303030303 -0.05050505051d + d2 = 0 + 0.303030303 Combine like terms: 0 + 0.303030303 = 0.303030303 -0.05050505051d + d2 = 0.303030303 The d term is -0.05050505051d. Take half its coefficient (-0.02525252526). Square it (0.0006376900320) and add it to both sides. Add '0.0006376900320' to each side of the equation. -0.05050505051d + 0.0006376900320 + d2 = 0.303030303 + 0.0006376900320 Reorder the terms: 0.0006376900320 + -0.05050505051d + d2 = 0.303030303 + 0.0006376900320 Combine like terms: 0.303030303 + 0.0006376900320 = 0.303667993032 0.0006376900320 + -0.05050505051d + d2 = 0.303667993032 Factor a perfect square on the left side: (d + -0.02525252526)(d + -0.02525252526) = 0.303667993032 Calculate the square root of the right side: 0.551060789 Break this problem into two subproblems by setting (d + -0.02525252526) equal to 0.551060789 and -0.551060789.Subproblem 1
d + -0.02525252526 = 0.551060789 Simplifying d + -0.02525252526 = 0.551060789 Reorder the terms: -0.02525252526 + d = 0.551060789 Solving -0.02525252526 + d = 0.551060789 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.02525252526' to each side of the equation. -0.02525252526 + 0.02525252526 + d = 0.551060789 + 0.02525252526 Combine like terms: -0.02525252526 + 0.02525252526 = 0.00000000000 0.00000000000 + d = 0.551060789 + 0.02525252526 d = 0.551060789 + 0.02525252526 Combine like terms: 0.551060789 + 0.02525252526 = 0.57631331426 d = 0.57631331426 Simplifying d = 0.57631331426Subproblem 2
d + -0.02525252526 = -0.551060789 Simplifying d + -0.02525252526 = -0.551060789 Reorder the terms: -0.02525252526 + d = -0.551060789 Solving -0.02525252526 + d = -0.551060789 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.02525252526' to each side of the equation. -0.02525252526 + 0.02525252526 + d = -0.551060789 + 0.02525252526 Combine like terms: -0.02525252526 + 0.02525252526 = 0.00000000000 0.00000000000 + d = -0.551060789 + 0.02525252526 d = -0.551060789 + 0.02525252526 Combine like terms: -0.551060789 + 0.02525252526 = -0.52580826374 d = -0.52580826374 Simplifying d = -0.52580826374Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.57631331426, -0.52580826374}
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