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Simplifying 0.8d2 + -2.4d + -125 = 0 Reorder the terms: -125 + -2.4d + 0.8d2 = 0 Solving -125 + -2.4d + 0.8d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -156.25 + -3d + d2 = 0 Move the constant term to the right: Add '156.25' to each side of the equation. -156.25 + -3d + 156.25 + d2 = 0 + 156.25 Reorder the terms: -156.25 + 156.25 + -3d + d2 = 0 + 156.25 Combine like terms: -156.25 + 156.25 = 0.00 0.00 + -3d + d2 = 0 + 156.25 -3d + d2 = 0 + 156.25 Combine like terms: 0 + 156.25 = 156.25 -3d + d2 = 156.25 The d term is -3d. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3d + 2.25 + d2 = 156.25 + 2.25 Reorder the terms: 2.25 + -3d + d2 = 156.25 + 2.25 Combine like terms: 156.25 + 2.25 = 158.5 2.25 + -3d + d2 = 158.5 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 158.5 Calculate the square root of the right side: 12.589678312 Break this problem into two subproblems by setting (d + -1.5) equal to 12.589678312 and -12.589678312.Subproblem 1
d + -1.5 = 12.589678312 Simplifying d + -1.5 = 12.589678312 Reorder the terms: -1.5 + d = 12.589678312 Solving -1.5 + d = 12.589678312 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = 12.589678312 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 12.589678312 + 1.5 d = 12.589678312 + 1.5 Combine like terms: 12.589678312 + 1.5 = 14.089678312 d = 14.089678312 Simplifying d = 14.089678312Subproblem 2
d + -1.5 = -12.589678312 Simplifying d + -1.5 = -12.589678312 Reorder the terms: -1.5 + d = -12.589678312 Solving -1.5 + d = -12.589678312 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = -12.589678312 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -12.589678312 + 1.5 d = -12.589678312 + 1.5 Combine like terms: -12.589678312 + 1.5 = -11.089678312 d = -11.089678312 Simplifying d = -11.089678312Solution
The solution to the problem is based on the solutions from the subproblems. d = {14.089678312, -11.089678312}
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