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Simplifying x2 + -11001x + -462000 = 0 Reorder the terms: -462000 + -11001x + x2 = 0 Solving -462000 + -11001x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '462000' to each side of the equation. -462000 + -11001x + 462000 + x2 = 0 + 462000 Reorder the terms: -462000 + 462000 + -11001x + x2 = 0 + 462000 Combine like terms: -462000 + 462000 = 0 0 + -11001x + x2 = 0 + 462000 -11001x + x2 = 0 + 462000 Combine like terms: 0 + 462000 = 462000 -11001x + x2 = 462000 The x term is -11001x. Take half its coefficient (-5500.5). Square it (30255500.25) and add it to both sides. Add '30255500.25' to each side of the equation. -11001x + 30255500.25 + x2 = 462000 + 30255500.25 Reorder the terms: 30255500.25 + -11001x + x2 = 462000 + 30255500.25 Combine like terms: 462000 + 30255500.25 = 30717500.25 30255500.25 + -11001x + x2 = 30717500.25 Factor a perfect square on the left side: (x + -5500.5)(x + -5500.5) = 30717500.25 Calculate the square root of the right side: 5542.337074737 Break this problem into two subproblems by setting (x + -5500.5) equal to 5542.337074737 and -5542.337074737.Subproblem 1
x + -5500.5 = 5542.337074737 Simplifying x + -5500.5 = 5542.337074737 Reorder the terms: -5500.5 + x = 5542.337074737 Solving -5500.5 + x = 5542.337074737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5500.5' to each side of the equation. -5500.5 + 5500.5 + x = 5542.337074737 + 5500.5 Combine like terms: -5500.5 + 5500.5 = 0.0 0.0 + x = 5542.337074737 + 5500.5 x = 5542.337074737 + 5500.5 Combine like terms: 5542.337074737 + 5500.5 = 11042.837074737 x = 11042.837074737 Simplifying x = 11042.837074737Subproblem 2
x + -5500.5 = -5542.337074737 Simplifying x + -5500.5 = -5542.337074737 Reorder the terms: -5500.5 + x = -5542.337074737 Solving -5500.5 + x = -5542.337074737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5500.5' to each side of the equation. -5500.5 + 5500.5 + x = -5542.337074737 + 5500.5 Combine like terms: -5500.5 + 5500.5 = 0.0 0.0 + x = -5542.337074737 + 5500.5 x = -5542.337074737 + 5500.5 Combine like terms: -5542.337074737 + 5500.5 = -41.837074737 x = -41.837074737 Simplifying x = -41.837074737Solution
The solution to the problem is based on the solutions from the subproblems. x = {11042.837074737, -41.837074737}
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