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Simplifying x2 + 2x + 1 = 40 Reorder the terms: 1 + 2x + x2 = 40 Solving 1 + 2x + x2 = 40 Solving for variable 'x'. Reorder the terms: 1 + -40 + 2x + x2 = 40 + -40 Combine like terms: 1 + -40 = -39 -39 + 2x + x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -39 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 2x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 2x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 2x + x2 = 0 + 39 2x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 2x + x2 = 39 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 = 39 + 1 Reorder the terms: 1 + 2x + x2 = 39 + 1 Combine like terms: 39 + 1 = 40 1 + 2x + x2 = 40 Factor a perfect square on the left side: (x + 1)(x + 1) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 1) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 1 = 6.32455532 Simplifying x + 1 = 6.32455532 Reorder the terms: 1 + x = 6.32455532 Solving 1 + x = 6.32455532 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 = 6.32455532 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.32455532 + -1 x = 6.32455532 + -1 Combine like terms: 6.32455532 + -1 = 5.32455532 x = 5.32455532 Simplifying x = 5.32455532Subproblem 2
x + 1 = -6.32455532 Simplifying x + 1 = -6.32455532 Reorder the terms: 1 + x = -6.32455532 Solving 1 + x = -6.32455532 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 = -6.32455532 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.32455532 + -1 x = -6.32455532 + -1 Combine like terms: -6.32455532 + -1 = -7.32455532 x = -7.32455532 Simplifying x = -7.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.32455532, -7.32455532}
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