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Simplifying 3d2 + -24d = 3 Reorder the terms: -24d + 3d2 = 3 Solving -24d + 3d2 = 3 Solving for variable 'd'. Reorder the terms: -3 + -24d + 3d2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -24d + 3d2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -8d + d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -8d + d2)' equal to zero and attempt to solve: Simplifying -1 + -8d + d2 = 0 Solving -1 + -8d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -8d + 1 + d2 = 0 + 1 Reorder the terms: -1 + 1 + -8d + d2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8d + d2 = 0 + 1 -8d + d2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8d + d2 = 1 The d term is -8d. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8d + 16 + d2 = 1 + 16 Reorder the terms: 16 + -8d + d2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + -8d + d2 = 17 Factor a perfect square on the left side: (d + -4)(d + -4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (d + -4) equal to 4.123105626 and -4.123105626.Subproblem 1
d + -4 = 4.123105626 Simplifying d + -4 = 4.123105626 Reorder the terms: -4 + d = 4.123105626 Solving -4 + d = 4.123105626 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = 4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + d = 4.123105626 + 4 d = 4.123105626 + 4 Combine like terms: 4.123105626 + 4 = 8.123105626 d = 8.123105626 Simplifying d = 8.123105626Subproblem 2
d + -4 = -4.123105626 Simplifying d + -4 = -4.123105626 Reorder the terms: -4 + d = -4.123105626 Solving -4 + d = -4.123105626 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = -4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + d = -4.123105626 + 4 d = -4.123105626 + 4 Combine like terms: -4.123105626 + 4 = -0.123105626 d = -0.123105626 Simplifying d = -0.123105626Solution
The solution to the problem is based on the solutions from the subproblems. d = {8.123105626, -0.123105626}Solution
d = {8.123105626, -0.123105626}
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