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Simplifying 1000 + -250x + x2 = 0 Solving 1000 + -250x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -250x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -250x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -250x + x2 = 0 + -1000 -250x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -250x + x2 = -1000 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 = -1000 + 15625 Reorder the terms: 15625 + -250x + x2 = -1000 + 15625 Combine like terms: -1000 + 15625 = 14625 15625 + -250x + x2 = 14625 Factor a perfect square on the left side: (x + -125)(x + -125) = 14625 Calculate the square root of the right side: 120.933866224 Break this problem into two subproblems by setting (x + -125) equal to 120.933866224 and -120.933866224.Subproblem 1
x + -125 = 120.933866224 Simplifying x + -125 = 120.933866224 Reorder the terms: -125 + x = 120.933866224 Solving -125 + x = 120.933866224 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 = 120.933866224 + 125 Combine like terms: -125 + 125 = 0 0 + x = 120.933866224 + 125 x = 120.933866224 + 125 Combine like terms: 120.933866224 + 125 = 245.933866224 x = 245.933866224 Simplifying x = 245.933866224Subproblem 2
x + -125 = -120.933866224 Simplifying x + -125 = -120.933866224 Reorder the terms: -125 + x = -120.933866224 Solving -125 + x = -120.933866224 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 = -120.933866224 + 125 Combine like terms: -125 + 125 = 0 0 + x = -120.933866224 + 125 x = -120.933866224 + 125 Combine like terms: -120.933866224 + 125 = 4.066133776 x = 4.066133776 Simplifying x = 4.066133776Solution
The solution to the problem is based on the solutions from the subproblems. x = {245.933866224, 4.066133776}
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