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Simplifying x4 + -2x2 + -45 = 0 Reorder the terms: -45 + -2x2 + x4 = 0 Solving -45 + -2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -2x2 + 45 + x4 = 0 + 45 Reorder the terms: -45 + 45 + -2x2 + x4 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -2x2 + x4 = 0 + 45 -2x2 + x4 = 0 + 45 Combine like terms: 0 + 45 = 45 -2x2 + x4 = 45 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 45 + 1 Reorder the terms: 1 + -2x2 + x4 = 45 + 1 Combine like terms: 45 + 1 = 46 1 + -2x2 + x4 = 46 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x2 + -1) equal to 6.782329983 and -6.782329983.Subproblem 1
x2 + -1 = 6.782329983 Simplifying x2 + -1 = 6.782329983 Reorder the terms: -1 + x2 = 6.782329983 Solving -1 + x2 = 6.782329983 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 + x2 = 6.782329983 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 6.782329983 + 1 x2 = 6.782329983 + 1 Combine like terms: 6.782329983 + 1 = 7.782329983 x2 = 7.782329983 Simplifying x2 = 7.782329983 Take the square root of each side: x = {-2.789682775, 2.789682775}Subproblem 2
x2 + -1 = -6.782329983 Simplifying x2 + -1 = -6.782329983 Reorder the terms: -1 + x2 = -6.782329983 Solving -1 + x2 = -6.782329983 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 + x2 = -6.782329983 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -6.782329983 + 1 x2 = -6.782329983 + 1 Combine like terms: -6.782329983 + 1 = -5.782329983 x2 = -5.782329983 Simplifying x2 = -5.782329983 Reorder the terms: 5.782329983 + x2 = -5.782329983 + 5.782329983 Combine like terms: -5.782329983 + 5.782329983 = 0.000000000 5.782329983 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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