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Simplifying x2 + -57x + 250 = 0 Reorder the terms: 250 + -57x + x2 = 0 Solving 250 + -57x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-250' to each side of the equation. 250 + -57x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + -57x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -57x + x2 = 0 + -250 -57x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 -57x + x2 = -250 The x term is -57x. Take half its coefficient (-28.5). Square it (812.25) and add it to both sides. Add '812.25' to each side of the equation. -57x + 812.25 + x2 = -250 + 812.25 Reorder the terms: 812.25 + -57x + x2 = -250 + 812.25 Combine like terms: -250 + 812.25 = 562.25 812.25 + -57x + x2 = 562.25 Factor a perfect square on the left side: (x + -28.5)(x + -28.5) = 562.25 Calculate the square root of the right side: 23.711811403 Break this problem into two subproblems by setting (x + -28.5) equal to 23.711811403 and -23.711811403.Subproblem 1
x + -28.5 = 23.711811403 Simplifying x + -28.5 = 23.711811403 Reorder the terms: -28.5 + x = 23.711811403 Solving -28.5 + x = 23.711811403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = 23.711811403 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = 23.711811403 + 28.5 x = 23.711811403 + 28.5 Combine like terms: 23.711811403 + 28.5 = 52.211811403 x = 52.211811403 Simplifying x = 52.211811403Subproblem 2
x + -28.5 = -23.711811403 Simplifying x + -28.5 = -23.711811403 Reorder the terms: -28.5 + x = -23.711811403 Solving -28.5 + x = -23.711811403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = -23.711811403 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = -23.711811403 + 28.5 x = -23.711811403 + 28.5 Combine like terms: -23.711811403 + 28.5 = 4.788188597 x = 4.788188597 Simplifying x = 4.788188597Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.211811403, 4.788188597}
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