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Simplifying 2d2 + -10d + -2 = 0 Reorder the terms: -2 + -10d + 2d2 = 0 Solving -2 + -10d + 2d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -5d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -5d + d2)' equal to zero and attempt to solve: Simplifying -1 + -5d + d2 = 0 Solving -1 + -5d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -5d + 1 + d2 = 0 + 1 Reorder the terms: -1 + 1 + -5d + d2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5d + d2 = 0 + 1 -5d + d2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5d + d2 = 1 The d term is -5d. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5d + 6.25 + d2 = 1 + 6.25 Reorder the terms: 6.25 + -5d + d2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + -5d + d2 = 7.25 Factor a perfect square on the left side: (d + -2.5)(d + -2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (d + -2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
d + -2.5 = 2.692582404 Simplifying d + -2.5 = 2.692582404 Reorder the terms: -2.5 + d = 2.692582404 Solving -2.5 + d = 2.692582404 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = 2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = 2.692582404 + 2.5 d = 2.692582404 + 2.5 Combine like terms: 2.692582404 + 2.5 = 5.192582404 d = 5.192582404 Simplifying d = 5.192582404Subproblem 2
d + -2.5 = -2.692582404 Simplifying d + -2.5 = -2.692582404 Reorder the terms: -2.5 + d = -2.692582404 Solving -2.5 + d = -2.692582404 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = -2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = -2.692582404 + 2.5 d = -2.692582404 + 2.5 Combine like terms: -2.692582404 + 2.5 = -0.192582404 d = -0.192582404 Simplifying d = -0.192582404Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.192582404, -0.192582404}Solution
d = {5.192582404, -0.192582404}
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