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Simplifying 3d2 + 36d + -123 = 0 Reorder the terms: -123 + 36d + 3d2 = 0 Solving -123 + 36d + 3d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '3'. 3(-41 + 12d + d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-41 + 12d + d2)' equal to zero and attempt to solve: Simplifying -41 + 12d + d2 = 0 Solving -41 + 12d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 12d + 41 + d2 = 0 + 41 Reorder the terms: -41 + 41 + 12d + d2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 12d + d2 = 0 + 41 12d + d2 = 0 + 41 Combine like terms: 0 + 41 = 41 12d + d2 = 41 The d term is 12d. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12d + 36 + d2 = 41 + 36 Reorder the terms: 36 + 12d + d2 = 41 + 36 Combine like terms: 41 + 36 = 77 36 + 12d + d2 = 77 Factor a perfect square on the left side: (d + 6)(d + 6) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (d + 6) equal to 8.774964387 and -8.774964387.Subproblem 1
d + 6 = 8.774964387 Simplifying d + 6 = 8.774964387 Reorder the terms: 6 + d = 8.774964387 Solving 6 + d = 8.774964387 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + d = 8.774964387 + -6 Combine like terms: 6 + -6 = 0 0 + d = 8.774964387 + -6 d = 8.774964387 + -6 Combine like terms: 8.774964387 + -6 = 2.774964387 d = 2.774964387 Simplifying d = 2.774964387Subproblem 2
d + 6 = -8.774964387 Simplifying d + 6 = -8.774964387 Reorder the terms: 6 + d = -8.774964387 Solving 6 + d = -8.774964387 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + d = -8.774964387 + -6 Combine like terms: 6 + -6 = 0 0 + d = -8.774964387 + -6 d = -8.774964387 + -6 Combine like terms: -8.774964387 + -6 = -14.774964387 d = -14.774964387 Simplifying d = -14.774964387Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.774964387, -14.774964387}Solution
d = {2.774964387, -14.774964387}
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