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Simplifying 2d2 + -7d + -5 = 0 Reorder the terms: -5 + -7d + 2d2 = 0 Solving -5 + -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'. -2.5 + -3.5d + d2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.5d + 2.5 + d2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.5d + d2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.5d + d2 = 0 + 2.5 -3.5d + d2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.5d + d2 = 2.5 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 = 2.5 + 3.0625 Reorder the terms: 3.0625 + -3.5d + d2 = 2.5 + 3.0625 Combine like terms: 2.5 + 3.0625 = 5.5625 3.0625 + -3.5d + d2 = 5.5625 Factor a perfect square on the left side: (d + -1.75)(d + -1.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (d + -1.75) equal to 2.358495283 and -2.358495283.Subproblem 1
d + -1.75 = 2.358495283 Simplifying d + -1.75 = 2.358495283 Reorder the terms: -1.75 + d = 2.358495283 Solving -1.75 + d = 2.358495283 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 = 2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + d = 2.358495283 + 1.75 d = 2.358495283 + 1.75 Combine like terms: 2.358495283 + 1.75 = 4.108495283 d = 4.108495283 Simplifying d = 4.108495283Subproblem 2
d + -1.75 = -2.358495283 Simplifying d + -1.75 = -2.358495283 Reorder the terms: -1.75 + d = -2.358495283 Solving -1.75 + d = -2.358495283 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 = -2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + d = -2.358495283 + 1.75 d = -2.358495283 + 1.75 Combine like terms: -2.358495283 + 1.75 = -0.608495283 d = -0.608495283 Simplifying d = -0.608495283Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.108495283, -0.608495283}
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