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Simplifying 200x + -1x2 = x2 + -195x + 4950 Reorder the terms: 200x + -1x2 = 4950 + -195x + x2 Solving 200x + -1x2 = 4950 + -195x + x2 Solving for variable 'x'. Reorder the terms: -4950 + 200x + 195x + -1x2 + -1x2 = 4950 + -195x + x2 + -4950 + 195x + -1x2 Combine like terms: 200x + 195x = 395x -4950 + 395x + -1x2 + -1x2 = 4950 + -195x + x2 + -4950 + 195x + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 -4950 + 395x + -2x2 = 4950 + -195x + x2 + -4950 + 195x + -1x2 Reorder the terms: -4950 + 395x + -2x2 = 4950 + -4950 + -195x + 195x + x2 + -1x2 Combine like terms: 4950 + -4950 = 0 -4950 + 395x + -2x2 = 0 + -195x + 195x + x2 + -1x2 -4950 + 395x + -2x2 = -195x + 195x + x2 + -1x2 Combine like terms: -195x + 195x = 0 -4950 + 395x + -2x2 = 0 + x2 + -1x2 -4950 + 395x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4950 + 395x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2475 + -197.5x + x2 = 0 Move the constant term to the right: Add '-2475' to each side of the equation. 2475 + -197.5x + -2475 + x2 = 0 + -2475 Reorder the terms: 2475 + -2475 + -197.5x + x2 = 0 + -2475 Combine like terms: 2475 + -2475 = 0 0 + -197.5x + x2 = 0 + -2475 -197.5x + x2 = 0 + -2475 Combine like terms: 0 + -2475 = -2475 -197.5x + x2 = -2475 The x term is -197.5x. Take half its coefficient (-98.75). Square it (9751.5625) and add it to both sides. Add '9751.5625' to each side of the equation. -197.5x + 9751.5625 + x2 = -2475 + 9751.5625 Reorder the terms: 9751.5625 + -197.5x + x2 = -2475 + 9751.5625 Combine like terms: -2475 + 9751.5625 = 7276.5625 9751.5625 + -197.5x + x2 = 7276.5625 Factor a perfect square on the left side: (x + -98.75)(x + -98.75) = 7276.5625 Calculate the square root of the right side: 85.302769592 Break this problem into two subproblems by setting (x + -98.75) equal to 85.302769592 and -85.302769592.Subproblem 1
x + -98.75 = 85.302769592 Simplifying x + -98.75 = 85.302769592 Reorder the terms: -98.75 + x = 85.302769592 Solving -98.75 + x = 85.302769592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98.75' to each side of the equation. -98.75 + 98.75 + x = 85.302769592 + 98.75 Combine like terms: -98.75 + 98.75 = 0.00 0.00 + x = 85.302769592 + 98.75 x = 85.302769592 + 98.75 Combine like terms: 85.302769592 + 98.75 = 184.052769592 x = 184.052769592 Simplifying x = 184.052769592Subproblem 2
x + -98.75 = -85.302769592 Simplifying x + -98.75 = -85.302769592 Reorder the terms: -98.75 + x = -85.302769592 Solving -98.75 + x = -85.302769592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98.75' to each side of the equation. -98.75 + 98.75 + x = -85.302769592 + 98.75 Combine like terms: -98.75 + 98.75 = 0.00 0.00 + x = -85.302769592 + 98.75 x = -85.302769592 + 98.75 Combine like terms: -85.302769592 + 98.75 = 13.447230408 x = 13.447230408 Simplifying x = 13.447230408Solution
The solution to the problem is based on the solutions from the subproblems. x = {184.052769592, 13.447230408}
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