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Simplifying x2 + 2x = 329 Reorder the terms: 2x + x2 = 329 Solving 2x + x2 = 329 Solving for variable 'x'. Reorder the terms: -329 + 2x + x2 = 329 + -329 Combine like terms: 329 + -329 = 0 -329 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '329' to each side of the equation. -329 + 2x + 329 + x2 = 0 + 329 Reorder the terms: -329 + 329 + 2x + x2 = 0 + 329 Combine like terms: -329 + 329 = 0 0 + 2x + x2 = 0 + 329 2x + x2 = 0 + 329 Combine like terms: 0 + 329 = 329 2x + x2 = 329 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 = 329 + 1 Reorder the terms: 1 + 2x + x2 = 329 + 1 Combine like terms: 329 + 1 = 330 1 + 2x + x2 = 330 Factor a perfect square on the left side: (x + 1)(x + 1) = 330 Calculate the square root of the right side: 18.165902125 Break this problem into two subproblems by setting (x + 1) equal to 18.165902125 and -18.165902125.Subproblem 1
x + 1 = 18.165902125 Simplifying x + 1 = 18.165902125 Reorder the terms: 1 + x = 18.165902125 Solving 1 + x = 18.165902125 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 = 18.165902125 + -1 Combine like terms: 1 + -1 = 0 0 + x = 18.165902125 + -1 x = 18.165902125 + -1 Combine like terms: 18.165902125 + -1 = 17.165902125 x = 17.165902125 Simplifying x = 17.165902125Subproblem 2
x + 1 = -18.165902125 Simplifying x + 1 = -18.165902125 Reorder the terms: 1 + x = -18.165902125 Solving 1 + x = -18.165902125 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 = -18.165902125 + -1 Combine like terms: 1 + -1 = 0 0 + x = -18.165902125 + -1 x = -18.165902125 + -1 Combine like terms: -18.165902125 + -1 = -19.165902125 x = -19.165902125 Simplifying x = -19.165902125Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.165902125, -19.165902125}
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