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Simplifying x4 + 4x2 + -36 = 0 Reorder the terms: -36 + 4x2 + x4 = 0 Solving -36 + 4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 4x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + 4x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 4x2 + x4 = 0 + 36 4x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 4x2 + x4 = 36 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 36 + 4 Reorder the terms: 4 + 4x2 + x4 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + 4x2 + x4 = 40 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x2 + 2) equal to 6.32455532 and -6.32455532.Subproblem 1
x2 + 2 = 6.32455532 Simplifying x2 + 2 = 6.32455532 Reorder the terms: 2 + x2 = 6.32455532 Solving 2 + x2 = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 6.32455532 + -2 x2 = 6.32455532 + -2 Combine like terms: 6.32455532 + -2 = 4.32455532 x2 = 4.32455532 Simplifying x2 = 4.32455532 Take the square root of each side: x = {-2.07955652, 2.07955652}Subproblem 2
x2 + 2 = -6.32455532 Simplifying x2 + 2 = -6.32455532 Reorder the terms: 2 + x2 = -6.32455532 Solving 2 + x2 = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -6.32455532 + -2 x2 = -6.32455532 + -2 Combine like terms: -6.32455532 + -2 = -8.32455532 x2 = -8.32455532 Simplifying x2 = -8.32455532 Reorder the terms: 8.32455532 + x2 = -8.32455532 + 8.32455532 Combine like terms: -8.32455532 + 8.32455532 = 0.00000000 8.32455532 + x2 = 0.00000000 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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