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Simplifying x(x + 200) = 1000 Reorder the terms: x(200 + x) = 1000 (200 * x + x * x) = 1000 (200x + x2) = 1000 Solving 200x + x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 200x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 200x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 200x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 200x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 200x + x2 = 0 + 1000 200x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 200x + x2 = 1000 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 = 1000 + 10000 Reorder the terms: 10000 + 200x + x2 = 1000 + 10000 Combine like terms: 1000 + 10000 = 11000 10000 + 200x + x2 = 11000 Factor a perfect square on the left side: (x + 100)(x + 100) = 11000 Calculate the square root of the right side: 104.880884817 Break this problem into two subproblems by setting (x + 100) equal to 104.880884817 and -104.880884817.Subproblem 1
x + 100 = 104.880884817 Simplifying x + 100 = 104.880884817 Reorder the terms: 100 + x = 104.880884817 Solving 100 + x = 104.880884817 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 = 104.880884817 + -100 Combine like terms: 100 + -100 = 0 0 + x = 104.880884817 + -100 x = 104.880884817 + -100 Combine like terms: 104.880884817 + -100 = 4.880884817 x = 4.880884817 Simplifying x = 4.880884817Subproblem 2
x + 100 = -104.880884817 Simplifying x + 100 = -104.880884817 Reorder the terms: 100 + x = -104.880884817 Solving 100 + x = -104.880884817 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 = -104.880884817 + -100 Combine like terms: 100 + -100 = 0 0 + x = -104.880884817 + -100 x = -104.880884817 + -100 Combine like terms: -104.880884817 + -100 = -204.880884817 x = -204.880884817 Simplifying x = -204.880884817Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.880884817, -204.880884817}
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