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Simplifying 3d2 + -12d = 57 Reorder the terms: -12d + 3d2 = 57 Solving -12d + 3d2 = 57 Solving for variable 'd'. Reorder the terms: -57 + -12d + 3d2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + -12d + 3d2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-19 + -4d + d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-19 + -4d + d2)' equal to zero and attempt to solve: Simplifying -19 + -4d + d2 = 0 Solving -19 + -4d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -4d + 19 + d2 = 0 + 19 Reorder the terms: -19 + 19 + -4d + d2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -4d + d2 = 0 + 19 -4d + d2 = 0 + 19 Combine like terms: 0 + 19 = 19 -4d + d2 = 19 The d term is -4d. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4d + 4 + d2 = 19 + 4 Reorder the terms: 4 + -4d + d2 = 19 + 4 Combine like terms: 19 + 4 = 23 4 + -4d + d2 = 23 Factor a perfect square on the left side: (d + -2)(d + -2) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (d + -2) equal to 4.795831523 and -4.795831523.Subproblem 1
d + -2 = 4.795831523 Simplifying d + -2 = 4.795831523 Reorder the terms: -2 + d = 4.795831523 Solving -2 + d = 4.795831523 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = 4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + d = 4.795831523 + 2 d = 4.795831523 + 2 Combine like terms: 4.795831523 + 2 = 6.795831523 d = 6.795831523 Simplifying d = 6.795831523Subproblem 2
d + -2 = -4.795831523 Simplifying d + -2 = -4.795831523 Reorder the terms: -2 + d = -4.795831523 Solving -2 + d = -4.795831523 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = -4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + d = -4.795831523 + 2 d = -4.795831523 + 2 Combine like terms: -4.795831523 + 2 = -2.795831523 d = -2.795831523 Simplifying d = -2.795831523Solution
The solution to the problem is based on the solutions from the subproblems. d = {6.795831523, -2.795831523}Solution
d = {6.795831523, -2.795831523}
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