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Simplifying 25x2 + -3000x + 36000 = 0 Reorder the terms: 36000 + -3000x + 25x2 = 0 Solving 36000 + -3000x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(1440 + -120x + x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(1440 + -120x + x2)' equal to zero and attempt to solve: Simplifying 1440 + -120x + x2 = 0 Solving 1440 + -120x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1440' to each side of the equation. 1440 + -120x + -1440 + x2 = 0 + -1440 Reorder the terms: 1440 + -1440 + -120x + x2 = 0 + -1440 Combine like terms: 1440 + -1440 = 0 0 + -120x + x2 = 0 + -1440 -120x + x2 = 0 + -1440 Combine like terms: 0 + -1440 = -1440 -120x + x2 = -1440 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -1440 + 3600 Reorder the terms: 3600 + -120x + x2 = -1440 + 3600 Combine like terms: -1440 + 3600 = 2160 3600 + -120x + x2 = 2160 Factor a perfect square on the left side: (x + -60)(x + -60) = 2160 Calculate the square root of the right side: 46.475800154 Break this problem into two subproblems by setting (x + -60) equal to 46.475800154 and -46.475800154.Subproblem 1
x + -60 = 46.475800154 Simplifying x + -60 = 46.475800154 Reorder the terms: -60 + x = 46.475800154 Solving -60 + x = 46.475800154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 46.475800154 + 60 Combine like terms: -60 + 60 = 0 0 + x = 46.475800154 + 60 x = 46.475800154 + 60 Combine like terms: 46.475800154 + 60 = 106.475800154 x = 106.475800154 Simplifying x = 106.475800154Subproblem 2
x + -60 = -46.475800154 Simplifying x + -60 = -46.475800154 Reorder the terms: -60 + x = -46.475800154 Solving -60 + x = -46.475800154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -46.475800154 + 60 Combine like terms: -60 + 60 = 0 0 + x = -46.475800154 + 60 x = -46.475800154 + 60 Combine like terms: -46.475800154 + 60 = 13.524199846 x = 13.524199846 Simplifying x = 13.524199846Solution
The solution to the problem is based on the solutions from the subproblems. x = {106.475800154, 13.524199846}Solution
x = {106.475800154, 13.524199846}
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