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Simplifying 250 + 125x + x2 = 1250 Solving 250 + 125x + x2 = 1250 Solving for variable 'x'. Reorder the terms: 250 + -1250 + 125x + x2 = 1250 + -1250 Combine like terms: 250 + -1250 = -1000 -1000 + 125x + x2 = 1250 + -1250 Combine like terms: 1250 + -1250 = 0 -1000 + 125x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 125x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 125x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 125x + x2 = 0 + 1000 125x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 125x + x2 = 1000 The x term is 125x. Take half its coefficient (62.5). Square it (3906.25) and add it to both sides. Add '3906.25' to each side of the equation. 125x + 3906.25 + x2 = 1000 + 3906.25 Reorder the terms: 3906.25 + 125x + x2 = 1000 + 3906.25 Combine like terms: 1000 + 3906.25 = 4906.25 3906.25 + 125x + x2 = 4906.25 Factor a perfect square on the left side: (x + 62.5)(x + 62.5) = 4906.25 Calculate the square root of the right side: 70.044628631 Break this problem into two subproblems by setting (x + 62.5) equal to 70.044628631 and -70.044628631.Subproblem 1
x + 62.5 = 70.044628631 Simplifying x + 62.5 = 70.044628631 Reorder the terms: 62.5 + x = 70.044628631 Solving 62.5 + x = 70.044628631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.5' to each side of the equation. 62.5 + -62.5 + x = 70.044628631 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + x = 70.044628631 + -62.5 x = 70.044628631 + -62.5 Combine like terms: 70.044628631 + -62.5 = 7.544628631 x = 7.544628631 Simplifying x = 7.544628631Subproblem 2
x + 62.5 = -70.044628631 Simplifying x + 62.5 = -70.044628631 Reorder the terms: 62.5 + x = -70.044628631 Solving 62.5 + x = -70.044628631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.5' to each side of the equation. 62.5 + -62.5 + x = -70.044628631 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + x = -70.044628631 + -62.5 x = -70.044628631 + -62.5 Combine like terms: -70.044628631 + -62.5 = -132.544628631 x = -132.544628631 Simplifying x = -132.544628631Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.544628631, -132.544628631}
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