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Simplifying x2 + 2x + -294 = 0 Reorder the terms: -294 + 2x + x2 = 0 Solving -294 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '294' to each side of the equation. -294 + 2x + 294 + x2 = 0 + 294 Reorder the terms: -294 + 294 + 2x + x2 = 0 + 294 Combine like terms: -294 + 294 = 0 0 + 2x + x2 = 0 + 294 2x + x2 = 0 + 294 Combine like terms: 0 + 294 = 294 2x + x2 = 294 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 = 294 + 1 Reorder the terms: 1 + 2x + x2 = 294 + 1 Combine like terms: 294 + 1 = 295 1 + 2x + x2 = 295 Factor a perfect square on the left side: (x + 1)(x + 1) = 295 Calculate the square root of the right side: 17.175564037 Break this problem into two subproblems by setting (x + 1) equal to 17.175564037 and -17.175564037.Subproblem 1
x + 1 = 17.175564037 Simplifying x + 1 = 17.175564037 Reorder the terms: 1 + x = 17.175564037 Solving 1 + x = 17.175564037 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 = 17.175564037 + -1 Combine like terms: 1 + -1 = 0 0 + x = 17.175564037 + -1 x = 17.175564037 + -1 Combine like terms: 17.175564037 + -1 = 16.175564037 x = 16.175564037 Simplifying x = 16.175564037Subproblem 2
x + 1 = -17.175564037 Simplifying x + 1 = -17.175564037 Reorder the terms: 1 + x = -17.175564037 Solving 1 + x = -17.175564037 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 = -17.175564037 + -1 Combine like terms: 1 + -1 = 0 0 + x = -17.175564037 + -1 x = -17.175564037 + -1 Combine like terms: -17.175564037 + -1 = -18.175564037 x = -18.175564037 Simplifying x = -18.175564037Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.175564037, -18.175564037}
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