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Simplifying -3.5d2 + 364d + -965 = 5135.50 Reorder the terms: -965 + 364d + -3.5d2 = 5135.50 Solving -965 + 364d + -3.5d2 = 5135.50 Solving for variable 'd'. Reorder the terms: -965 + -5135.50 + 364d + -3.5d2 = 5135.50 + -5135.50 Combine like terms: -965 + -5135.50 = -6100.5 -6100.5 + 364d + -3.5d2 = 5135.50 + -5135.50 Combine like terms: 5135.50 + -5135.50 = 0.00 -6100.5 + 364d + -3.5d2 = 0.00 Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. 1743 + -104d + d2 = 0.0 Move the constant term to the right: Add '-1743' to each side of the equation. 1743 + -104d + -1743 + d2 = 0.0 + -1743 Reorder the terms: 1743 + -1743 + -104d + d2 = 0.0 + -1743 Combine like terms: 1743 + -1743 = 0 0 + -104d + d2 = 0.0 + -1743 -104d + d2 = 0.0 + -1743 Combine like terms: 0.0 + -1743 = -1743 -104d + d2 = -1743 The d term is -104d. Take half its coefficient (-52). Square it (2704) and add it to both sides. Add '2704' to each side of the equation. -104d + 2704 + d2 = -1743 + 2704 Reorder the terms: 2704 + -104d + d2 = -1743 + 2704 Combine like terms: -1743 + 2704 = 961 2704 + -104d + d2 = 961 Factor a perfect square on the left side: (d + -52)(d + -52) = 961 Calculate the square root of the right side: 31 Break this problem into two subproblems by setting (d + -52) equal to 31 and -31.Subproblem 1
d + -52 = 31 Simplifying d + -52 = 31 Reorder the terms: -52 + d = 31 Solving -52 + d = 31 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + d = 31 + 52 Combine like terms: -52 + 52 = 0 0 + d = 31 + 52 d = 31 + 52 Combine like terms: 31 + 52 = 83 d = 83 Simplifying d = 83Subproblem 2
d + -52 = -31 Simplifying d + -52 = -31 Reorder the terms: -52 + d = -31 Solving -52 + d = -31 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + d = -31 + 52 Combine like terms: -52 + 52 = 0 0 + d = -31 + 52 d = -31 + 52 Combine like terms: -31 + 52 = 21 d = 21 Simplifying d = 21Solution
The solution to the problem is based on the solutions from the subproblems. d = {83, 21}
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