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Simplifying x2 + -4096x + -4096 = 0 Reorder the terms: -4096 + -4096x + x2 = 0 Solving -4096 + -4096x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4096' to each side of the equation. -4096 + -4096x + 4096 + x2 = 0 + 4096 Reorder the terms: -4096 + 4096 + -4096x + x2 = 0 + 4096 Combine like terms: -4096 + 4096 = 0 0 + -4096x + x2 = 0 + 4096 -4096x + x2 = 0 + 4096 Combine like terms: 0 + 4096 = 4096 -4096x + x2 = 4096 The x term is -4096x. Take half its coefficient (-2048). Square it (4194304) and add it to both sides. Add '4194304' to each side of the equation. -4096x + 4194304 + x2 = 4096 + 4194304 Reorder the terms: 4194304 + -4096x + x2 = 4096 + 4194304 Combine like terms: 4096 + 4194304 = 4198400 4194304 + -4096x + x2 = 4198400 Factor a perfect square on the left side: (x + -2048)(x + -2048) = 4198400 Calculate the square root of the right side: 2048.999755979 Break this problem into two subproblems by setting (x + -2048) equal to 2048.999755979 and -2048.999755979.Subproblem 1
x + -2048 = 2048.999755979 Simplifying x + -2048 = 2048.999755979 Reorder the terms: -2048 + x = 2048.999755979 Solving -2048 + x = 2048.999755979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2048' to each side of the equation. -2048 + 2048 + x = 2048.999755979 + 2048 Combine like terms: -2048 + 2048 = 0 0 + x = 2048.999755979 + 2048 x = 2048.999755979 + 2048 Combine like terms: 2048.999755979 + 2048 = 4096.999755979 x = 4096.999755979 Simplifying x = 4096.999755979Subproblem 2
x + -2048 = -2048.999755979 Simplifying x + -2048 = -2048.999755979 Reorder the terms: -2048 + x = -2048.999755979 Solving -2048 + x = -2048.999755979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2048' to each side of the equation. -2048 + 2048 + x = -2048.999755979 + 2048 Combine like terms: -2048 + 2048 = 0 0 + x = -2048.999755979 + 2048 x = -2048.999755979 + 2048 Combine like terms: -2048.999755979 + 2048 = -0.999755979 x = -0.999755979 Simplifying x = -0.999755979Solution
The solution to the problem is based on the solutions from the subproblems. x = {4096.999755979, -0.999755979}
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