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Simplifying 2d2 = 8 + 2d Solving 2d2 = 8 + 2d Solving for variable 'd'. Reorder the terms: -8 + -2d + 2d2 = 8 + 2d + -8 + -2d Reorder the terms: -8 + -2d + 2d2 = 8 + -8 + 2d + -2d Combine like terms: 8 + -8 = 0 -8 + -2d + 2d2 = 0 + 2d + -2d -8 + -2d + 2d2 = 2d + -2d Combine like terms: 2d + -2d = 0 -8 + -2d + 2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -1d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1d + d2)' equal to zero and attempt to solve: Simplifying -4 + -1d + d2 = 0 Solving -4 + -1d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -1d + 4 + d2 = 0 + 4 Reorder the terms: -4 + 4 + -1d + d2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1d + d2 = 0 + 4 -1d + d2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1d + d2 = 4 The d term is -1d. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1d + 0.25 + d2 = 4 + 0.25 Reorder the terms: 0.25 + -1d + d2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + -1d + d2 = 4.25 Factor a perfect square on the left side: (d + -0.5)(d + -0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (d + -0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
d + -0.5 = 2.061552813 Simplifying d + -0.5 = 2.061552813 Reorder the terms: -0.5 + d = 2.061552813 Solving -0.5 + d = 2.061552813 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = 2.061552813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = 2.061552813 + 0.5 d = 2.061552813 + 0.5 Combine like terms: 2.061552813 + 0.5 = 2.561552813 d = 2.561552813 Simplifying d = 2.561552813Subproblem 2
d + -0.5 = -2.061552813 Simplifying d + -0.5 = -2.061552813 Reorder the terms: -0.5 + d = -2.061552813 Solving -0.5 + d = -2.061552813 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = -2.061552813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = -2.061552813 + 0.5 d = -2.061552813 + 0.5 Combine like terms: -2.061552813 + 0.5 = -1.561552813 d = -1.561552813 Simplifying d = -1.561552813Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.561552813, -1.561552813}Solution
d = {2.561552813, -1.561552813}
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