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Simplifying 2d2 + -6d = 10 Reorder the terms: -6d + 2d2 = 10 Solving -6d + 2d2 = 10 Solving for variable 'd'. Reorder the terms: -10 + -6d + 2d2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -6d + 2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -3d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -3d + d2)' equal to zero and attempt to solve: Simplifying -5 + -3d + d2 = 0 Solving -5 + -3d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -3d + 5 + d2 = 0 + 5 Reorder the terms: -5 + 5 + -3d + d2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3d + d2 = 0 + 5 -3d + d2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3d + d2 = 5 The d term is -3d. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3d + 2.25 + d2 = 5 + 2.25 Reorder the terms: 2.25 + -3d + d2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + -3d + d2 = 7.25 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (d + -1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
d + -1.5 = 2.692582404 Simplifying d + -1.5 = 2.692582404 Reorder the terms: -1.5 + d = 2.692582404 Solving -1.5 + d = 2.692582404 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = 2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 2.692582404 + 1.5 d = 2.692582404 + 1.5 Combine like terms: 2.692582404 + 1.5 = 4.192582404 d = 4.192582404 Simplifying d = 4.192582404Subproblem 2
d + -1.5 = -2.692582404 Simplifying d + -1.5 = -2.692582404 Reorder the terms: -1.5 + d = -2.692582404 Solving -1.5 + d = -2.692582404 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = -2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -2.692582404 + 1.5 d = -2.692582404 + 1.5 Combine like terms: -2.692582404 + 1.5 = -1.192582404 d = -1.192582404 Simplifying d = -1.192582404Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.192582404, -1.192582404}Solution
d = {4.192582404, -1.192582404}
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