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Simplifying 2d2 + 48d = 98 Reorder the terms: 48d + 2d2 = 98 Solving 48d + 2d2 = 98 Solving for variable 'd'. Reorder the terms: -98 + 48d + 2d2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 48d + 2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + 24d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + 24d + d2)' equal to zero and attempt to solve: Simplifying -49 + 24d + d2 = 0 Solving -49 + 24d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 24d + 49 + d2 = 0 + 49 Reorder the terms: -49 + 49 + 24d + d2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 24d + d2 = 0 + 49 24d + d2 = 0 + 49 Combine like terms: 0 + 49 = 49 24d + d2 = 49 The d term is 24d. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24d + 144 + d2 = 49 + 144 Reorder the terms: 144 + 24d + d2 = 49 + 144 Combine like terms: 49 + 144 = 193 144 + 24d + d2 = 193 Factor a perfect square on the left side: (d + 12)(d + 12) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (d + 12) equal to 13.892443989 and -13.892443989.Subproblem 1
d + 12 = 13.892443989 Simplifying d + 12 = 13.892443989 Reorder the terms: 12 + d = 13.892443989 Solving 12 + d = 13.892443989 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + d = 13.892443989 + -12 Combine like terms: 12 + -12 = 0 0 + d = 13.892443989 + -12 d = 13.892443989 + -12 Combine like terms: 13.892443989 + -12 = 1.892443989 d = 1.892443989 Simplifying d = 1.892443989Subproblem 2
d + 12 = -13.892443989 Simplifying d + 12 = -13.892443989 Reorder the terms: 12 + d = -13.892443989 Solving 12 + d = -13.892443989 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + d = -13.892443989 + -12 Combine like terms: 12 + -12 = 0 0 + d = -13.892443989 + -12 d = -13.892443989 + -12 Combine like terms: -13.892443989 + -12 = -25.892443989 d = -25.892443989 Simplifying d = -25.892443989Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.892443989, -25.892443989}Solution
d = {1.892443989, -25.892443989}
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