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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 = -10.5572809 x = -10.5572809 Simplifying x = -10.5572809Subproblem 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 = -189.4427191 x = -189.4427191 Simplifying x = -189.4427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.5572809, -189.4427191}
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