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Simplifying x2 + -200x + -2000 = 0 Reorder the terms: -2000 + -200x + x2 = 0 Solving -2000 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + -200x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -200x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -200x + x2 = 0 + 2000 -200x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -200x + x2 = 2000 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = 2000 + 10000 Reorder the terms: 10000 + -200x + x2 = 2000 + 10000 Combine like terms: 2000 + 10000 = 12000 10000 + -200x + x2 = 12000 Factor a perfect square on the left side: (x + -100)(x + -100) = 12000 Calculate the square root of the right side: 109.544511501 Break this problem into two subproblems by setting (x + -100) equal to 109.544511501 and -109.544511501.Subproblem 1
x + -100 = 109.544511501 Simplifying x + -100 = 109.544511501 Reorder the terms: -100 + x = 109.544511501 Solving -100 + x = 109.544511501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 109.544511501 + 100 Combine like terms: -100 + 100 = 0 0 + x = 109.544511501 + 100 x = 109.544511501 + 100 Combine like terms: 109.544511501 + 100 = 209.544511501 x = 209.544511501 Simplifying x = 209.544511501Subproblem 2
x + -100 = -109.544511501 Simplifying x + -100 = -109.544511501 Reorder the terms: -100 + x = -109.544511501 Solving -100 + x = -109.544511501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -109.544511501 + 100 Combine like terms: -100 + 100 = 0 0 + x = -109.544511501 + 100 x = -109.544511501 + 100 Combine like terms: -109.544511501 + 100 = -9.544511501 x = -9.544511501 Simplifying x = -9.544511501Solution
The solution to the problem is based on the solutions from the subproblems. x = {209.544511501, -9.544511501}
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