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Simplifying x2 + -200x + -10200 = 0 Reorder the terms: -10200 + -200x + x2 = 0 Solving -10200 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10200' to each side of the equation. -10200 + -200x + 10200 + x2 = 0 + 10200 Reorder the terms: -10200 + 10200 + -200x + x2 = 0 + 10200 Combine like terms: -10200 + 10200 = 0 0 + -200x + x2 = 0 + 10200 -200x + x2 = 0 + 10200 Combine like terms: 0 + 10200 = 10200 -200x + x2 = 10200 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 = 10200 + 10000 Reorder the terms: 10000 + -200x + x2 = 10200 + 10000 Combine like terms: 10200 + 10000 = 20200 10000 + -200x + x2 = 20200 Factor a perfect square on the left side: (x + -100)(x + -100) = 20200 Calculate the square root of the right side: 142.126704036 Break this problem into two subproblems by setting (x + -100) equal to 142.126704036 and -142.126704036.Subproblem 1
x + -100 = 142.126704036 Simplifying x + -100 = 142.126704036 Reorder the terms: -100 + x = 142.126704036 Solving -100 + x = 142.126704036 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 = 142.126704036 + 100 Combine like terms: -100 + 100 = 0 0 + x = 142.126704036 + 100 x = 142.126704036 + 100 Combine like terms: 142.126704036 + 100 = 242.126704036 x = 242.126704036 Simplifying x = 242.126704036Subproblem 2
x + -100 = -142.126704036 Simplifying x + -100 = -142.126704036 Reorder the terms: -100 + x = -142.126704036 Solving -100 + x = -142.126704036 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 = -142.126704036 + 100 Combine like terms: -100 + 100 = 0 0 + x = -142.126704036 + 100 x = -142.126704036 + 100 Combine like terms: -142.126704036 + 100 = -42.126704036 x = -42.126704036 Simplifying x = -42.126704036Solution
The solution to the problem is based on the solutions from the subproblems. x = {242.126704036, -42.126704036}
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