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Simplifying -16d2 + 1000d + 50 = 0 Reorder the terms: 50 + 1000d + -16d2 = 0 Solving 50 + 1000d + -16d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 500d + -8d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 500d + -8d2)' equal to zero and attempt to solve: Simplifying 25 + 500d + -8d2 = 0 Solving 25 + 500d + -8d2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -62.5d + d2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -62.5d + 3.125 + d2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -62.5d + d2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -62.5d + d2 = 0 + 3.125 -62.5d + d2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -62.5d + d2 = 3.125 The d term is -62.5d. Take half its coefficient (-31.25). Square it (976.5625) and add it to both sides. Add '976.5625' to each side of the equation. -62.5d + 976.5625 + d2 = 3.125 + 976.5625 Reorder the terms: 976.5625 + -62.5d + d2 = 3.125 + 976.5625 Combine like terms: 3.125 + 976.5625 = 979.6875 976.5625 + -62.5d + d2 = 979.6875 Factor a perfect square on the left side: (d + -31.25)(d + -31.25) = 979.6875 Calculate the square root of the right side: 31.299960064 Break this problem into two subproblems by setting (d + -31.25) equal to 31.299960064 and -31.299960064.Subproblem 1
d + -31.25 = 31.299960064 Simplifying d + -31.25 = 31.299960064 Reorder the terms: -31.25 + d = 31.299960064 Solving -31.25 + d = 31.299960064 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '31.25' to each side of the equation. -31.25 + 31.25 + d = 31.299960064 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + d = 31.299960064 + 31.25 d = 31.299960064 + 31.25 Combine like terms: 31.299960064 + 31.25 = 62.549960064 d = 62.549960064 Simplifying d = 62.549960064Subproblem 2
d + -31.25 = -31.299960064 Simplifying d + -31.25 = -31.299960064 Reorder the terms: -31.25 + d = -31.299960064 Solving -31.25 + d = -31.299960064 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '31.25' to each side of the equation. -31.25 + 31.25 + d = -31.299960064 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + d = -31.299960064 + 31.25 d = -31.299960064 + 31.25 Combine like terms: -31.299960064 + 31.25 = -0.049960064 d = -0.049960064 Simplifying d = -0.049960064Solution
The solution to the problem is based on the solutions from the subproblems. d = {62.549960064, -0.049960064}Solution
d = {62.549960064, -0.049960064}
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