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Simplifying -4d2 + 8d = -52 Reorder the terms: 8d + -4d2 = -52 Solving 8d + -4d2 = -52 Solving for variable 'd'. Reorder the terms: 52 + 8d + -4d2 = -52 + 52 Combine like terms: -52 + 52 = 0 52 + 8d + -4d2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(13 + 2d + -1d2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(13 + 2d + -1d2)' equal to zero and attempt to solve: Simplifying 13 + 2d + -1d2 = 0 Solving 13 + 2d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -2d + d2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -2d + 13 + d2 = 0 + 13 Reorder the terms: -13 + 13 + -2d + d2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2d + d2 = 0 + 13 -2d + d2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2d + d2 = 13 The d term is -2d. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2d + 1 + d2 = 13 + 1 Reorder the terms: 1 + -2d + d2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + -2d + d2 = 14 Factor a perfect square on the left side: (d + -1)(d + -1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (d + -1) equal to 3.741657387 and -3.741657387.Subproblem 1
d + -1 = 3.741657387 Simplifying d + -1 = 3.741657387 Reorder the terms: -1 + d = 3.741657387 Solving -1 + d = 3.741657387 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + d = 3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + d = 3.741657387 + 1 d = 3.741657387 + 1 Combine like terms: 3.741657387 + 1 = 4.741657387 d = 4.741657387 Simplifying d = 4.741657387Subproblem 2
d + -1 = -3.741657387 Simplifying d + -1 = -3.741657387 Reorder the terms: -1 + d = -3.741657387 Solving -1 + d = -3.741657387 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + d = -3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + d = -3.741657387 + 1 d = -3.741657387 + 1 Combine like terms: -3.741657387 + 1 = -2.741657387 d = -2.741657387 Simplifying d = -2.741657387Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.741657387, -2.741657387}Solution
d = {4.741657387, -2.741657387}
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