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Simplifying 8d2 + -7d + -3 = 0 Reorder the terms: -3 + -7d + 8d2 = 0 Solving -3 + -7d + 8d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -0.875d + d2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.875d + 0.375 + d2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.875d + d2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.875d + d2 = 0 + 0.375 -0.875d + d2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.875d + d2 = 0.375 The d term is -0.875d. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875d + 0.19140625 + d2 = 0.375 + 0.19140625 Reorder the terms: 0.19140625 + -0.875d + d2 = 0.375 + 0.19140625 Combine like terms: 0.375 + 0.19140625 = 0.56640625 0.19140625 + -0.875d + d2 = 0.56640625 Factor a perfect square on the left side: (d + -0.4375)(d + -0.4375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (d + -0.4375) equal to 0.752599661 and -0.752599661.Subproblem 1
d + -0.4375 = 0.752599661 Simplifying d + -0.4375 = 0.752599661 Reorder the terms: -0.4375 + d = 0.752599661 Solving -0.4375 + d = 0.752599661 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + d = 0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + d = 0.752599661 + 0.4375 d = 0.752599661 + 0.4375 Combine like terms: 0.752599661 + 0.4375 = 1.190099661 d = 1.190099661 Simplifying d = 1.190099661Subproblem 2
d + -0.4375 = -0.752599661 Simplifying d + -0.4375 = -0.752599661 Reorder the terms: -0.4375 + d = -0.752599661 Solving -0.4375 + d = -0.752599661 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + d = -0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + d = -0.752599661 + 0.4375 d = -0.752599661 + 0.4375 Combine like terms: -0.752599661 + 0.4375 = -0.315099661 d = -0.315099661 Simplifying d = -0.315099661Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.190099661, -0.315099661}
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