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Simplifying 2d2 + 12d + -16 = 0 Reorder the terms: -16 + 12d + 2d2 = 0 Solving -16 + 12d + 2d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 6d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 6d + d2)' equal to zero and attempt to solve: Simplifying -8 + 6d + d2 = 0 Solving -8 + 6d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 6d + 8 + d2 = 0 + 8 Reorder the terms: -8 + 8 + 6d + d2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6d + d2 = 0 + 8 6d + d2 = 0 + 8 Combine like terms: 0 + 8 = 8 6d + d2 = 8 The d term is 6d. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6d + 9 + d2 = 8 + 9 Reorder the terms: 9 + 6d + d2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6d + d2 = 17 Factor a perfect square on the left side: (d + 3)(d + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (d + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
d + 3 = 4.123105626 Simplifying d + 3 = 4.123105626 Reorder the terms: 3 + d = 4.123105626 Solving 3 + d = 4.123105626 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + d = 4.123105626 + -3 d = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 d = 1.123105626 Simplifying d = 1.123105626Subproblem 2
d + 3 = -4.123105626 Simplifying d + 3 = -4.123105626 Reorder the terms: 3 + d = -4.123105626 Solving 3 + d = -4.123105626 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + d = -4.123105626 + -3 d = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 d = -7.123105626 Simplifying d = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.123105626, -7.123105626}Solution
d = {1.123105626, -7.123105626}
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