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Simplifying x2 + 2x + -44 = 0 Reorder the terms: -44 + 2x + x2 = 0 Solving -44 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 2x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 2x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 2x + x2 = 0 + 44 2x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 2x + x2 = 44 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 = 44 + 1 Reorder the terms: 1 + 2x + x2 = 44 + 1 Combine like terms: 44 + 1 = 45 1 + 2x + x2 = 45 Factor a perfect square on the left side: (x + 1)(x + 1) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 1) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 1 = 6.708203933 Simplifying x + 1 = 6.708203933 Reorder the terms: 1 + x = 6.708203933 Solving 1 + x = 6.708203933 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 = 6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.708203933 + -1 x = 6.708203933 + -1 Combine like terms: 6.708203933 + -1 = 5.708203933 x = 5.708203933 Simplifying x = 5.708203933Subproblem 2
x + 1 = -6.708203933 Simplifying x + 1 = -6.708203933 Reorder the terms: 1 + x = -6.708203933 Solving 1 + x = -6.708203933 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 = -6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.708203933 + -1 x = -6.708203933 + -1 Combine like terms: -6.708203933 + -1 = -7.708203933 x = -7.708203933 Simplifying x = -7.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.708203933, -7.708203933}
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