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Simplifying 44.8 = 20d + d2 Solving 44.8 = 20d + d2 Solving for variable 'd'. Reorder the terms: 44.8 + -20d + -1d2 = 20d + -20d + d2 + -1d2 Combine like terms: 20d + -20d = 0 44.8 + -20d + -1d2 = 0 + d2 + -1d2 44.8 + -20d + -1d2 = d2 + -1d2 Combine like terms: d2 + -1d2 = 0 44.8 + -20d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44.8 + 20d + d2 = 0 Move the constant term to the right: Add '44.8' to each side of the equation. -44.8 + 20d + 44.8 + d2 = 0 + 44.8 Reorder the terms: -44.8 + 44.8 + 20d + d2 = 0 + 44.8 Combine like terms: -44.8 + 44.8 = 0.0 0.0 + 20d + d2 = 0 + 44.8 20d + d2 = 0 + 44.8 Combine like terms: 0 + 44.8 = 44.8 20d + d2 = 44.8 The d term is 20d. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20d + 100 + d2 = 44.8 + 100 Reorder the terms: 100 + 20d + d2 = 44.8 + 100 Combine like terms: 44.8 + 100 = 144.8 100 + 20d + d2 = 144.8 Factor a perfect square on the left side: (d + 10)(d + 10) = 144.8 Calculate the square root of the right side: 12.033287165 Break this problem into two subproblems by setting (d + 10) equal to 12.033287165 and -12.033287165.Subproblem 1
d + 10 = 12.033287165 Simplifying d + 10 = 12.033287165 Reorder the terms: 10 + d = 12.033287165 Solving 10 + d = 12.033287165 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + d = 12.033287165 + -10 Combine like terms: 10 + -10 = 0 0 + d = 12.033287165 + -10 d = 12.033287165 + -10 Combine like terms: 12.033287165 + -10 = 2.033287165 d = 2.033287165 Simplifying d = 2.033287165Subproblem 2
d + 10 = -12.033287165 Simplifying d + 10 = -12.033287165 Reorder the terms: 10 + d = -12.033287165 Solving 10 + d = -12.033287165 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + d = -12.033287165 + -10 Combine like terms: 10 + -10 = 0 0 + d = -12.033287165 + -10 d = -12.033287165 + -10 Combine like terms: -12.033287165 + -10 = -22.033287165 d = -22.033287165 Simplifying d = -22.033287165Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.033287165, -22.033287165}
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