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Simplifying 7d2 + 3d + -1 = 0 Reorder the terms: -1 + 3d + 7d2 = 0 Solving -1 + 3d + 7d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + 0.4285714286d + d2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.4285714286d + 0.1428571429 + d2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.4285714286d + d2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.4285714286d + d2 = 0 + 0.1428571429 0.4285714286d + d2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.4285714286d + d2 = 0.1428571429 The d term is 0.4285714286d. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286d + 0.04591836735 + d2 = 0.1428571429 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286d + d2 = 0.1428571429 + 0.04591836735 Combine like terms: 0.1428571429 + 0.04591836735 = 0.18877551025 0.04591836735 + 0.4285714286d + d2 = 0.18877551025 Factor a perfect square on the left side: (d + 0.2142857143)(d + 0.2142857143) = 0.18877551025 Calculate the square root of the right side: 0.434483038 Break this problem into two subproblems by setting (d + 0.2142857143) equal to 0.434483038 and -0.434483038.Subproblem 1
d + 0.2142857143 = 0.434483038 Simplifying d + 0.2142857143 = 0.434483038 Reorder the terms: 0.2142857143 + d = 0.434483038 Solving 0.2142857143 + d = 0.434483038 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + d = 0.434483038 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + d = 0.434483038 + -0.2142857143 d = 0.434483038 + -0.2142857143 Combine like terms: 0.434483038 + -0.2142857143 = 0.2201973237 d = 0.2201973237 Simplifying d = 0.2201973237Subproblem 2
d + 0.2142857143 = -0.434483038 Simplifying d + 0.2142857143 = -0.434483038 Reorder the terms: 0.2142857143 + d = -0.434483038 Solving 0.2142857143 + d = -0.434483038 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + d = -0.434483038 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + d = -0.434483038 + -0.2142857143 d = -0.434483038 + -0.2142857143 Combine like terms: -0.434483038 + -0.2142857143 = -0.6487687523 d = -0.6487687523 Simplifying d = -0.6487687523Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.2201973237, -0.6487687523}
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