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Simplifying x4 + 12x2 + -36 = 0 Reorder the terms: -36 + 12x2 + x4 = 0 Solving -36 + 12x2 + 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 + 12x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + 12x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 12x2 + x4 = 0 + 36 12x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 12x2 + x4 = 36 The x term is 12x2. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x2 + 36 + x4 = 36 + 36 Reorder the terms: 36 + 12x2 + x4 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + 12x2 + x4 = 72 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x2 + 6) equal to 8.485281374 and -8.485281374.Subproblem 1
x2 + 6 = 8.485281374 Simplifying x2 + 6 = 8.485281374 Reorder the terms: 6 + x2 = 8.485281374 Solving 6 + x2 = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 8.485281374 + -6 x2 = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 x2 = 2.485281374 Simplifying x2 = 2.485281374 Take the square root of each side: x = {-1.576477521, 1.576477521}Subproblem 2
x2 + 6 = -8.485281374 Simplifying x2 + 6 = -8.485281374 Reorder the terms: 6 + x2 = -8.485281374 Solving 6 + x2 = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -8.485281374 + -6 x2 = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 x2 = -14.485281374 Simplifying x2 = -14.485281374 Reorder the terms: 14.485281374 + x2 = -14.485281374 + 14.485281374 Combine like terms: -14.485281374 + 14.485281374 = 0.000000000 14.485281374 + 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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