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Simplifying 7d2 + -9d + 1 = 0 Reorder the terms: 1 + -9d + 7d2 = 0 Solving 1 + -9d + 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 + -1.285714286d + d2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -1.285714286d + -0.1428571429 + d2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -1.285714286d + d2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -1.285714286d + d2 = 0 + -0.1428571429 -1.285714286d + d2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -1.285714286d + d2 = -0.1428571429 The d term is -1.285714286d. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286d + 0.4132653063 + d2 = -0.1428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286d + d2 = -0.1428571429 + 0.4132653063 Combine like terms: -0.1428571429 + 0.4132653063 = 0.2704081634 0.4132653063 + -1.285714286d + d2 = 0.2704081634 Factor a perfect square on the left side: (d + -0.642857143)(d + -0.642857143) = 0.2704081634 Calculate the square root of the right side: 0.520007849 Break this problem into two subproblems by setting (d + -0.642857143) equal to 0.520007849 and -0.520007849.Subproblem 1
d + -0.642857143 = 0.520007849 Simplifying d + -0.642857143 = 0.520007849 Reorder the terms: -0.642857143 + d = 0.520007849 Solving -0.642857143 + d = 0.520007849 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + d = 0.520007849 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + d = 0.520007849 + 0.642857143 d = 0.520007849 + 0.642857143 Combine like terms: 0.520007849 + 0.642857143 = 1.162864992 d = 1.162864992 Simplifying d = 1.162864992Subproblem 2
d + -0.642857143 = -0.520007849 Simplifying d + -0.642857143 = -0.520007849 Reorder the terms: -0.642857143 + d = -0.520007849 Solving -0.642857143 + d = -0.520007849 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + d = -0.520007849 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + d = -0.520007849 + 0.642857143 d = -0.520007849 + 0.642857143 Combine like terms: -0.520007849 + 0.642857143 = 0.122849294 d = 0.122849294 Simplifying d = 0.122849294Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.162864992, 0.122849294}
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