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Simplifying x2 + -250x + 5000 = 0 Reorder the terms: 5000 + -250x + x2 = 0 Solving 5000 + -250x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -250x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -250x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -250x + x2 = 0 + -5000 -250x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -250x + x2 = -5000 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = -5000 + 15625 Reorder the terms: 15625 + -250x + x2 = -5000 + 15625 Combine like terms: -5000 + 15625 = 10625 15625 + -250x + x2 = 10625 Factor a perfect square on the left side: (x + -125)(x + -125) = 10625 Calculate the square root of the right side: 103.07764064 Break this problem into two subproblems by setting (x + -125) equal to 103.07764064 and -103.07764064.Subproblem 1
x + -125 = 103.07764064 Simplifying x + -125 = 103.07764064 Reorder the terms: -125 + x = 103.07764064 Solving -125 + x = 103.07764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 103.07764064 + 125 Combine like terms: -125 + 125 = 0 0 + x = 103.07764064 + 125 x = 103.07764064 + 125 Combine like terms: 103.07764064 + 125 = 228.07764064 x = 228.07764064 Simplifying x = 228.07764064Subproblem 2
x + -125 = -103.07764064 Simplifying x + -125 = -103.07764064 Reorder the terms: -125 + x = -103.07764064 Solving -125 + x = -103.07764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -103.07764064 + 125 Combine like terms: -125 + 125 = 0 0 + x = -103.07764064 + 125 x = -103.07764064 + 125 Combine like terms: -103.07764064 + 125 = 21.92235936 x = 21.92235936 Simplifying x = 21.92235936Solution
The solution to the problem is based on the solutions from the subproblems. x = {228.07764064, 21.92235936}
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