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Simplifying 0.8d2 + 2.4d + -115 = 0 Reorder the terms: -115 + 2.4d + 0.8d2 = 0 Solving -115 + 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'. -143.75 + 3d + d2 = 0 Move the constant term to the right: Add '143.75' to each side of the equation. -143.75 + 3d + 143.75 + d2 = 0 + 143.75 Reorder the terms: -143.75 + 143.75 + 3d + d2 = 0 + 143.75 Combine like terms: -143.75 + 143.75 = 0.00 0.00 + 3d + d2 = 0 + 143.75 3d + d2 = 0 + 143.75 Combine like terms: 0 + 143.75 = 143.75 3d + d2 = 143.75 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 = 143.75 + 2.25 Reorder the terms: 2.25 + 3d + d2 = 143.75 + 2.25 Combine like terms: 143.75 + 2.25 = 146 2.25 + 3d + d2 = 146 Factor a perfect square on the left side: (d + 1.5)(d + 1.5) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (d + 1.5) equal to 12.083045974 and -12.083045974.Subproblem 1
d + 1.5 = 12.083045974 Simplifying d + 1.5 = 12.083045974 Reorder the terms: 1.5 + d = 12.083045974 Solving 1.5 + d = 12.083045974 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 = 12.083045974 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + d = 12.083045974 + -1.5 d = 12.083045974 + -1.5 Combine like terms: 12.083045974 + -1.5 = 10.583045974 d = 10.583045974 Simplifying d = 10.583045974Subproblem 2
d + 1.5 = -12.083045974 Simplifying d + 1.5 = -12.083045974 Reorder the terms: 1.5 + d = -12.083045974 Solving 1.5 + d = -12.083045974 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 = -12.083045974 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + d = -12.083045974 + -1.5 d = -12.083045974 + -1.5 Combine like terms: -12.083045974 + -1.5 = -13.583045974 d = -13.583045974 Simplifying d = -13.583045974Solution
The solution to the problem is based on the solutions from the subproblems. d = {10.583045974, -13.583045974}
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