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Simplifying 2d2 + -2d + -675 = 0 Reorder the terms: -675 + -2d + 2d2 = 0 Solving -675 + -2d + 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'. -337.5 + -1d + d2 = 0 Move the constant term to the right: Add '337.5' to each side of the equation. -337.5 + -1d + 337.5 + d2 = 0 + 337.5 Reorder the terms: -337.5 + 337.5 + -1d + d2 = 0 + 337.5 Combine like terms: -337.5 + 337.5 = 0.0 0.0 + -1d + d2 = 0 + 337.5 -1d + d2 = 0 + 337.5 Combine like terms: 0 + 337.5 = 337.5 -1d + d2 = 337.5 The d term is -1d. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1d + 0.25 + d2 = 337.5 + 0.25 Reorder the terms: 0.25 + -1d + d2 = 337.5 + 0.25 Combine like terms: 337.5 + 0.25 = 337.75 0.25 + -1d + d2 = 337.75 Factor a perfect square on the left side: (d + -0.5)(d + -0.5) = 337.75 Calculate the square root of the right side: 18.377975949 Break this problem into two subproblems by setting (d + -0.5) equal to 18.377975949 and -18.377975949.Subproblem 1
d + -0.5 = 18.377975949 Simplifying d + -0.5 = 18.377975949 Reorder the terms: -0.5 + d = 18.377975949 Solving -0.5 + d = 18.377975949 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = 18.377975949 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = 18.377975949 + 0.5 d = 18.377975949 + 0.5 Combine like terms: 18.377975949 + 0.5 = 18.877975949 d = 18.877975949 Simplifying d = 18.877975949Subproblem 2
d + -0.5 = -18.377975949 Simplifying d + -0.5 = -18.377975949 Reorder the terms: -0.5 + d = -18.377975949 Solving -0.5 + d = -18.377975949 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = -18.377975949 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = -18.377975949 + 0.5 d = -18.377975949 + 0.5 Combine like terms: -18.377975949 + 0.5 = -17.877975949 d = -17.877975949 Simplifying d = -17.877975949Solution
The solution to the problem is based on the solutions from the subproblems. d = {18.877975949, -17.877975949}
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