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Simplifying 3d2 + 24d + -39 = 0 Reorder the terms: -39 + 24d + 3d2 = 0 Solving -39 + 24d + 3d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 8d + d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + 8d + d2)' equal to zero and attempt to solve: Simplifying -13 + 8d + d2 = 0 Solving -13 + 8d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 8d + 13 + d2 = 0 + 13 Reorder the terms: -13 + 13 + 8d + d2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 8d + d2 = 0 + 13 8d + d2 = 0 + 13 Combine like terms: 0 + 13 = 13 8d + d2 = 13 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 = 13 + 16 Reorder the terms: 16 + 8d + d2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + 8d + d2 = 29 Factor a perfect square on the left side: (d + 4)(d + 4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (d + 4) equal to 5.385164807 and -5.385164807.Subproblem 1
d + 4 = 5.385164807 Simplifying d + 4 = 5.385164807 Reorder the terms: 4 + d = 5.385164807 Solving 4 + d = 5.385164807 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 = 5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + d = 5.385164807 + -4 d = 5.385164807 + -4 Combine like terms: 5.385164807 + -4 = 1.385164807 d = 1.385164807 Simplifying d = 1.385164807Subproblem 2
d + 4 = -5.385164807 Simplifying d + 4 = -5.385164807 Reorder the terms: 4 + d = -5.385164807 Solving 4 + d = -5.385164807 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 = -5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + d = -5.385164807 + -4 d = -5.385164807 + -4 Combine like terms: -5.385164807 + -4 = -9.385164807 d = -9.385164807 Simplifying d = -9.385164807Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.385164807, -9.385164807}Solution
d = {1.385164807, -9.385164807}
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