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Simplifying (x2) + 201061x + 10106000000 = 0 x2 + 201061x + 10106000000 = 0 Reorder the terms: 10106000000 + 201061x + x2 = 0 Solving 10106000000 + 201061x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10106000000' to each side of the equation. 10106000000 + 201061x + -10106000000 + x2 = 0 + -10106000000 Reorder the terms: 10106000000 + -10106000000 + 201061x + x2 = 0 + -10106000000 Combine like terms: 10106000000 + -10106000000 = 0 0 + 201061x + x2 = 0 + -10106000000 201061x + x2 = 0 + -10106000000 Combine like terms: 0 + -10106000000 = -10106000000 201061x + x2 = -10106000000 The x term is 201061x. Take half its coefficient (100530.5). Square it (10106381430) and add it to both sides. Add '10106381430' to each side of the equation. 201061x + 10106381430 + x2 = -10106000000 + 10106381430 Reorder the terms: 10106381430 + 201061x + x2 = -10106000000 + 10106381430 Combine like terms: -10106000000 + 10106381430 = 381430 10106381430 + 201061x + x2 = 381430 Factor a perfect square on the left side: (x + 100530.5)(x + 100530.5) = 381430 Calculate the square root of the right side: 617.6001943 Break this problem into two subproblems by setting (x + 100530.5) equal to 617.6001943 and -617.6001943.Subproblem 1
x + 100530.5 = 617.6001943 Simplifying x + 100530.5 = 617.6001943 Reorder the terms: 100530.5 + x = 617.6001943 Solving 100530.5 + x = 617.6001943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100530.5' to each side of the equation. 100530.5 + -100530.5 + x = 617.6001943 + -100530.5 Combine like terms: 100530.5 + -100530.5 = 0.0 0.0 + x = 617.6001943 + -100530.5 x = 617.6001943 + -100530.5 Combine like terms: 617.6001943 + -100530.5 = -99912.8998057 x = -99912.8998057 Simplifying x = -99912.8998057Subproblem 2
x + 100530.5 = -617.6001943 Simplifying x + 100530.5 = -617.6001943 Reorder the terms: 100530.5 + x = -617.6001943 Solving 100530.5 + x = -617.6001943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100530.5' to each side of the equation. 100530.5 + -100530.5 + x = -617.6001943 + -100530.5 Combine like terms: 100530.5 + -100530.5 = 0.0 0.0 + x = -617.6001943 + -100530.5 x = -617.6001943 + -100530.5 Combine like terms: -617.6001943 + -100530.5 = -101148.1001943 x = -101148.1001943 Simplifying x = -101148.1001943Solution
The solution to the problem is based on the solutions from the subproblems. x = {-99912.8998057, -101148.1001943}
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