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Simplifying x2 + 2x = 256 Reorder the terms: 2x + x2 = 256 Solving 2x + x2 = 256 Solving for variable 'x'. Reorder the terms: -256 + 2x + x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 2x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 2x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 2x + x2 = 0 + 256 2x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 2x + x2 = 256 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 256 + 1 Reorder the terms: 1 + 2x + x2 = 256 + 1 Combine like terms: 256 + 1 = 257 1 + 2x + x2 = 257 Factor a perfect square on the left side: (x + 1)(x + 1) = 257 Calculate the square root of the right side: 16.031219542 Break this problem into two subproblems by setting (x + 1) equal to 16.031219542 and -16.031219542.Subproblem 1
x + 1 = 16.031219542 Simplifying x + 1 = 16.031219542 Reorder the terms: 1 + x = 16.031219542 Solving 1 + x = 16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 16.031219542 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.031219542 + -1 x = 16.031219542 + -1 Combine like terms: 16.031219542 + -1 = 15.031219542 x = 15.031219542 Simplifying x = 15.031219542Subproblem 2
x + 1 = -16.031219542 Simplifying x + 1 = -16.031219542 Reorder the terms: 1 + x = -16.031219542 Solving 1 + x = -16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -16.031219542 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.031219542 + -1 x = -16.031219542 + -1 Combine like terms: -16.031219542 + -1 = -17.031219542 x = -17.031219542 Simplifying x = -17.031219542Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.031219542, -17.031219542}
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