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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 = 8000 10000 + -200x + x2 = 8000 Factor a perfect square on the left side: (x + -100)(x + -100) = 8000 Calculate the square root of the right side: 89.4427191 Break this problem into two subproblems by setting (x + -100) equal to 89.4427191 and -89.4427191.Subproblem 1
x + -100 = 89.4427191 Simplifying x + -100 = 89.4427191 Reorder the terms: -100 + x = 89.4427191 Solving -100 + x = 89.4427191 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 = 89.4427191 + 100 Combine like terms: -100 + 100 = 0 0 + x = 89.4427191 + 100 x = 89.4427191 + 100 Combine like terms: 89.4427191 + 100 = 189.4427191 x = 189.4427191 Simplifying x = 189.4427191Subproblem 2
x + -100 = -89.4427191 Simplifying x + -100 = -89.4427191 Reorder the terms: -100 + x = -89.4427191 Solving -100 + x = -89.4427191 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 = -89.4427191 + 100 Combine like terms: -100 + 100 = 0 0 + x = -89.4427191 + 100 x = -89.4427191 + 100 Combine like terms: -89.4427191 + 100 = 10.5572809 x = 10.5572809 Simplifying x = 10.5572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {189.4427191, 10.5572809}
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