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Simplifying 2d2 + 7d + -2 = 0 Reorder the terms: -2 + 7d + 2d2 = 0 Solving -2 + 7d + 2d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 3.5d + d2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3.5d + 1 + d2 = 0 + 1 Reorder the terms: -1 + 1 + 3.5d + d2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3.5d + d2 = 0 + 1 3.5d + d2 = 0 + 1 Combine like terms: 0 + 1 = 1 3.5d + d2 = 1 The d term is 3.5d. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5d + 3.0625 + d2 = 1 + 3.0625 Reorder the terms: 3.0625 + 3.5d + d2 = 1 + 3.0625 Combine like terms: 1 + 3.0625 = 4.0625 3.0625 + 3.5d + d2 = 4.0625 Factor a perfect square on the left side: (d + 1.75)(d + 1.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (d + 1.75) equal to 2.015564437 and -2.015564437.Subproblem 1
d + 1.75 = 2.015564437 Simplifying d + 1.75 = 2.015564437 Reorder the terms: 1.75 + d = 2.015564437 Solving 1.75 + d = 2.015564437 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + d = 2.015564437 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + d = 2.015564437 + -1.75 d = 2.015564437 + -1.75 Combine like terms: 2.015564437 + -1.75 = 0.265564437 d = 0.265564437 Simplifying d = 0.265564437Subproblem 2
d + 1.75 = -2.015564437 Simplifying d + 1.75 = -2.015564437 Reorder the terms: 1.75 + d = -2.015564437 Solving 1.75 + d = -2.015564437 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + d = -2.015564437 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + d = -2.015564437 + -1.75 d = -2.015564437 + -1.75 Combine like terms: -2.015564437 + -1.75 = -3.765564437 d = -3.765564437 Simplifying d = -3.765564437Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.265564437, -3.765564437}
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