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Simplifying 2d2 = 6 + 10d Solving 2d2 = 6 + 10d Solving for variable 'd'. Reorder the terms: -6 + -10d + 2d2 = 6 + 10d + -6 + -10d Reorder the terms: -6 + -10d + 2d2 = 6 + -6 + 10d + -10d Combine like terms: 6 + -6 = 0 -6 + -10d + 2d2 = 0 + 10d + -10d -6 + -10d + 2d2 = 10d + -10d Combine like terms: 10d + -10d = 0 -6 + -10d + 2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -5d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -5d + d2)' equal to zero and attempt to solve: Simplifying -3 + -5d + d2 = 0 Solving -3 + -5d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -5d + 3 + d2 = 0 + 3 Reorder the terms: -3 + 3 + -5d + d2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5d + d2 = 0 + 3 -5d + d2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5d + d2 = 3 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 = 3 + 6.25 Reorder the terms: 6.25 + -5d + d2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + -5d + d2 = 9.25 Factor a perfect square on the left side: (d + -2.5)(d + -2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (d + -2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
d + -2.5 = 3.041381265 Simplifying d + -2.5 = 3.041381265 Reorder the terms: -2.5 + d = 3.041381265 Solving -2.5 + d = 3.041381265 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 = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = 3.041381265 + 2.5 d = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 d = 5.541381265 Simplifying d = 5.541381265Subproblem 2
d + -2.5 = -3.041381265 Simplifying d + -2.5 = -3.041381265 Reorder the terms: -2.5 + d = -3.041381265 Solving -2.5 + d = -3.041381265 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 = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = -3.041381265 + 2.5 d = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 d = -0.541381265 Simplifying d = -0.541381265Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.541381265, -0.541381265}Solution
d = {5.541381265, -0.541381265}
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