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Simplifying 5d2 + -112d + 80 = 0 Reorder the terms: 80 + -112d + 5d2 = 0 Solving 80 + -112d + 5d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 16 + -22.4d + d2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -22.4d + -16 + d2 = 0 + -16 Reorder the terms: 16 + -16 + -22.4d + d2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -22.4d + d2 = 0 + -16 -22.4d + d2 = 0 + -16 Combine like terms: 0 + -16 = -16 -22.4d + d2 = -16 The d term is -22.4d. Take half its coefficient (-11.2). Square it (125.44) and add it to both sides. Add '125.44' to each side of the equation. -22.4d + 125.44 + d2 = -16 + 125.44 Reorder the terms: 125.44 + -22.4d + d2 = -16 + 125.44 Combine like terms: -16 + 125.44 = 109.44 125.44 + -22.4d + d2 = 109.44 Factor a perfect square on the left side: (d + -11.2)(d + -11.2) = 109.44 Calculate the square root of the right side: 10.461357464 Break this problem into two subproblems by setting (d + -11.2) equal to 10.461357464 and -10.461357464.Subproblem 1
d + -11.2 = 10.461357464 Simplifying d + -11.2 = 10.461357464 Reorder the terms: -11.2 + d = 10.461357464 Solving -11.2 + d = 10.461357464 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '11.2' to each side of the equation. -11.2 + 11.2 + d = 10.461357464 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + d = 10.461357464 + 11.2 d = 10.461357464 + 11.2 Combine like terms: 10.461357464 + 11.2 = 21.661357464 d = 21.661357464 Simplifying d = 21.661357464Subproblem 2
d + -11.2 = -10.461357464 Simplifying d + -11.2 = -10.461357464 Reorder the terms: -11.2 + d = -10.461357464 Solving -11.2 + d = -10.461357464 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '11.2' to each side of the equation. -11.2 + 11.2 + d = -10.461357464 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + d = -10.461357464 + 11.2 d = -10.461357464 + 11.2 Combine like terms: -10.461357464 + 11.2 = 0.738642536 d = 0.738642536 Simplifying d = 0.738642536Solution
The solution to the problem is based on the solutions from the subproblems. d = {21.661357464, 0.738642536}
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