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Simplifying x2 + -200x + 8000 = 0 Reorder the terms: 8000 + -200x + x2 = 0 Solving 8000 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8000' to each side of the equation. 8000 + -200x + -8000 + x2 = 0 + -8000 Reorder the terms: 8000 + -8000 + -200x + x2 = 0 + -8000 Combine like terms: 8000 + -8000 = 0 0 + -200x + x2 = 0 + -8000 -200x + x2 = 0 + -8000 Combine like terms: 0 + -8000 = -8000 -200x + x2 = -8000 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 = -8000 + 10000 Reorder the terms: 10000 + -200x + x2 = -8000 + 10000 Combine like terms: -8000 + 10000 = 2000 10000 + -200x + x2 = 2000 Factor a perfect square on the left side: (x + -100)(x + -100) = 2000 Calculate the square root of the right side: 44.72135955 Break this problem into two subproblems by setting (x + -100) equal to 44.72135955 and -44.72135955.Subproblem 1
x + -100 = 44.72135955 Simplifying x + -100 = 44.72135955 Reorder the terms: -100 + x = 44.72135955 Solving -100 + x = 44.72135955 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 = 44.72135955 + 100 Combine like terms: -100 + 100 = 0 0 + x = 44.72135955 + 100 x = 44.72135955 + 100 Combine like terms: 44.72135955 + 100 = 144.72135955 x = 144.72135955 Simplifying x = 144.72135955Subproblem 2
x + -100 = -44.72135955 Simplifying x + -100 = -44.72135955 Reorder the terms: -100 + x = -44.72135955 Solving -100 + x = -44.72135955 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 = -44.72135955 + 100 Combine like terms: -100 + 100 = 0 0 + x = -44.72135955 + 100 x = -44.72135955 + 100 Combine like terms: -44.72135955 + 100 = 55.27864045 x = 55.27864045 Simplifying x = 55.27864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.72135955, 55.27864045}
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