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Simplifying 95 = 0.8d2 + -2.4d Reorder the terms: 95 = -2.4d + 0.8d2 Solving 95 = -2.4d + 0.8d2 Solving for variable 'd'. Reorder the terms: 95 + 2.4d + -0.8d2 = -2.4d + 2.4d + 0.8d2 + -0.8d2 Combine like terms: -2.4d + 2.4d = 0.0 95 + 2.4d + -0.8d2 = 0.0 + 0.8d2 + -0.8d2 95 + 2.4d + -0.8d2 = 0.8d2 + -0.8d2 Combine like terms: 0.8d2 + -0.8d2 = 0.0 95 + 2.4d + -0.8d2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -118.75 + -3d + d2 = 0 Move the constant term to the right: Add '118.75' to each side of the equation. -118.75 + -3d + 118.75 + d2 = 0 + 118.75 Reorder the terms: -118.75 + 118.75 + -3d + d2 = 0 + 118.75 Combine like terms: -118.75 + 118.75 = 0.00 0.00 + -3d + d2 = 0 + 118.75 -3d + d2 = 0 + 118.75 Combine like terms: 0 + 118.75 = 118.75 -3d + d2 = 118.75 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 = 118.75 + 2.25 Reorder the terms: 2.25 + -3d + d2 = 118.75 + 2.25 Combine like terms: 118.75 + 2.25 = 121 2.25 + -3d + d2 = 121 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 121 Calculate the square root of the right side: 11 Break this problem into two subproblems by setting (d + -1.5) equal to 11 and -11.Subproblem 1
d + -1.5 = 11 Simplifying d + -1.5 = 11 Reorder the terms: -1.5 + d = 11 Solving -1.5 + d = 11 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 = 11 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 11 + 1.5 d = 11 + 1.5 Combine like terms: 11 + 1.5 = 12.5 d = 12.5 Simplifying d = 12.5Subproblem 2
d + -1.5 = -11 Simplifying d + -1.5 = -11 Reorder the terms: -1.5 + d = -11 Solving -1.5 + d = -11 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 = -11 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -11 + 1.5 d = -11 + 1.5 Combine like terms: -11 + 1.5 = -9.5 d = -9.5 Simplifying d = -9.5Solution
The solution to the problem is based on the solutions from the subproblems. d = {12.5, -9.5}
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