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Simplifying x2 + 200x + -5000 = 0 Reorder the terms: -5000 + 200x + x2 = 0 Solving -5000 + 200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 200x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 200x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 200x + x2 = 0 + 5000 200x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 200x + x2 = 5000 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 = 5000 + 10000 Reorder the terms: 10000 + 200x + x2 = 5000 + 10000 Combine like terms: 5000 + 10000 = 15000 10000 + 200x + x2 = 15000 Factor a perfect square on the left side: (x + 100)(x + 100) = 15000 Calculate the square root of the right side: 122.474487139 Break this problem into two subproblems by setting (x + 100) equal to 122.474487139 and -122.474487139.Subproblem 1
x + 100 = 122.474487139 Simplifying x + 100 = 122.474487139 Reorder the terms: 100 + x = 122.474487139 Solving 100 + x = 122.474487139 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 = 122.474487139 + -100 Combine like terms: 100 + -100 = 0 0 + x = 122.474487139 + -100 x = 122.474487139 + -100 Combine like terms: 122.474487139 + -100 = 22.474487139 x = 22.474487139 Simplifying x = 22.474487139Subproblem 2
x + 100 = -122.474487139 Simplifying x + 100 = -122.474487139 Reorder the terms: 100 + x = -122.474487139 Solving 100 + x = -122.474487139 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 = -122.474487139 + -100 Combine like terms: 100 + -100 = 0 0 + x = -122.474487139 + -100 x = -122.474487139 + -100 Combine like terms: -122.474487139 + -100 = -222.474487139 x = -222.474487139 Simplifying x = -222.474487139Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.474487139, -222.474487139}
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