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Simplifying 0 = 0.02d2 + -2.6d + 66.5 Reorder the terms: 0 = 66.5 + -2.6d + 0.02d2 Solving 0 = 66.5 + -2.6d + 0.02d2 Solving for variable 'd'. Combine like terms: 0 + -66.5 = -66.5 -66.5 + 2.6d + -0.02d2 = 66.5 + -2.6d + 0.02d2 + -66.5 + 2.6d + -0.02d2 Reorder the terms: -66.5 + 2.6d + -0.02d2 = 66.5 + -66.5 + -2.6d + 2.6d + 0.02d2 + -0.02d2 Combine like terms: 66.5 + -66.5 = 0.0 -66.5 + 2.6d + -0.02d2 = 0.0 + -2.6d + 2.6d + 0.02d2 + -0.02d2 -66.5 + 2.6d + -0.02d2 = -2.6d + 2.6d + 0.02d2 + -0.02d2 Combine like terms: -2.6d + 2.6d = 0.0 -66.5 + 2.6d + -0.02d2 = 0.0 + 0.02d2 + -0.02d2 -66.5 + 2.6d + -0.02d2 = 0.02d2 + -0.02d2 Combine like terms: 0.02d2 + -0.02d2 = 0.00 -66.5 + 2.6d + -0.02d2 = 0.00 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 3325 + -130d + d2 = 0 Move the constant term to the right: Add '-3325' to each side of the equation. 3325 + -130d + -3325 + d2 = 0 + -3325 Reorder the terms: 3325 + -3325 + -130d + d2 = 0 + -3325 Combine like terms: 3325 + -3325 = 0 0 + -130d + d2 = 0 + -3325 -130d + d2 = 0 + -3325 Combine like terms: 0 + -3325 = -3325 -130d + d2 = -3325 The d term is -130d. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130d + 4225 + d2 = -3325 + 4225 Reorder the terms: 4225 + -130d + d2 = -3325 + 4225 Combine like terms: -3325 + 4225 = 900 4225 + -130d + d2 = 900 Factor a perfect square on the left side: (d + -65)(d + -65) = 900 Calculate the square root of the right side: 30 Break this problem into two subproblems by setting (d + -65) equal to 30 and -30.Subproblem 1
d + -65 = 30 Simplifying d + -65 = 30 Reorder the terms: -65 + d = 30 Solving -65 + d = 30 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + d = 30 + 65 Combine like terms: -65 + 65 = 0 0 + d = 30 + 65 d = 30 + 65 Combine like terms: 30 + 65 = 95 d = 95 Simplifying d = 95Subproblem 2
d + -65 = -30 Simplifying d + -65 = -30 Reorder the terms: -65 + d = -30 Solving -65 + d = -30 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + d = -30 + 65 Combine like terms: -65 + 65 = 0 0 + d = -30 + 65 d = -30 + 65 Combine like terms: -30 + 65 = 35 d = 35 Simplifying d = 35Solution
The solution to the problem is based on the solutions from the subproblems. d = {95, 35}
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