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Simplifying 2d2 + -48d = 14 Reorder the terms: -48d + 2d2 = 14 Solving -48d + 2d2 = 14 Solving for variable 'd'. Reorder the terms: -14 + -48d + 2d2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -48d + 2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -24d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -24d + d2)' equal to zero and attempt to solve: Simplifying -7 + -24d + d2 = 0 Solving -7 + -24d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -24d + 7 + d2 = 0 + 7 Reorder the terms: -7 + 7 + -24d + d2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -24d + d2 = 0 + 7 -24d + d2 = 0 + 7 Combine like terms: 0 + 7 = 7 -24d + d2 = 7 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 = 7 + 144 Reorder the terms: 144 + -24d + d2 = 7 + 144 Combine like terms: 7 + 144 = 151 144 + -24d + d2 = 151 Factor a perfect square on the left side: (d + -12)(d + -12) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (d + -12) equal to 12.288205727 and -12.288205727.Subproblem 1
d + -12 = 12.288205727 Simplifying d + -12 = 12.288205727 Reorder the terms: -12 + d = 12.288205727 Solving -12 + d = 12.288205727 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 = 12.288205727 + 12 Combine like terms: -12 + 12 = 0 0 + d = 12.288205727 + 12 d = 12.288205727 + 12 Combine like terms: 12.288205727 + 12 = 24.288205727 d = 24.288205727 Simplifying d = 24.288205727Subproblem 2
d + -12 = -12.288205727 Simplifying d + -12 = -12.288205727 Reorder the terms: -12 + d = -12.288205727 Solving -12 + d = -12.288205727 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 = -12.288205727 + 12 Combine like terms: -12 + 12 = 0 0 + d = -12.288205727 + 12 d = -12.288205727 + 12 Combine like terms: -12.288205727 + 12 = -0.288205727 d = -0.288205727 Simplifying d = -0.288205727Solution
The solution to the problem is based on the solutions from the subproblems. d = {24.288205727, -0.288205727}Solution
d = {24.288205727, -0.288205727}
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