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Simplifying 2d2 + 56d + -86 = 0 Reorder the terms: -86 + 56d + 2d2 = 0 Solving -86 + 56d + 2d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-43 + 28d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-43 + 28d + d2)' equal to zero and attempt to solve: Simplifying -43 + 28d + d2 = 0 Solving -43 + 28d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 28d + 43 + d2 = 0 + 43 Reorder the terms: -43 + 43 + 28d + d2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 28d + d2 = 0 + 43 28d + d2 = 0 + 43 Combine like terms: 0 + 43 = 43 28d + d2 = 43 The d term is 28d. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28d + 196 + d2 = 43 + 196 Reorder the terms: 196 + 28d + d2 = 43 + 196 Combine like terms: 43 + 196 = 239 196 + 28d + d2 = 239 Factor a perfect square on the left side: (d + 14)(d + 14) = 239 Calculate the square root of the right side: 15.459624834 Break this problem into two subproblems by setting (d + 14) equal to 15.459624834 and -15.459624834.Subproblem 1
d + 14 = 15.459624834 Simplifying d + 14 = 15.459624834 Reorder the terms: 14 + d = 15.459624834 Solving 14 + d = 15.459624834 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + d = 15.459624834 + -14 Combine like terms: 14 + -14 = 0 0 + d = 15.459624834 + -14 d = 15.459624834 + -14 Combine like terms: 15.459624834 + -14 = 1.459624834 d = 1.459624834 Simplifying d = 1.459624834Subproblem 2
d + 14 = -15.459624834 Simplifying d + 14 = -15.459624834 Reorder the terms: 14 + d = -15.459624834 Solving 14 + d = -15.459624834 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + d = -15.459624834 + -14 Combine like terms: 14 + -14 = 0 0 + d = -15.459624834 + -14 d = -15.459624834 + -14 Combine like terms: -15.459624834 + -14 = -29.459624834 d = -29.459624834 Simplifying d = -29.459624834Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.459624834, -29.459624834}Solution
d = {1.459624834, -29.459624834}
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