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Simplifying x4 + 12x2 + -27 = 0 Reorder the terms: -27 + 12x2 + x4 = 0 Solving -27 + 12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 12x2 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + 12x2 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 12x2 + x4 = 0 + 27 12x2 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 12x2 + x4 = 27 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 = 27 + 36 Reorder the terms: 36 + 12x2 + x4 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + 12x2 + x4 = 63 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x2 + 6) equal to 7.937253933 and -7.937253933.Subproblem 1
x2 + 6 = 7.937253933 Simplifying x2 + 6 = 7.937253933 Reorder the terms: 6 + x2 = 7.937253933 Solving 6 + x2 = 7.937253933 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 = 7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 7.937253933 + -6 x2 = 7.937253933 + -6 Combine like terms: 7.937253933 + -6 = 1.937253933 x2 = 1.937253933 Simplifying x2 = 1.937253933 Take the square root of each side: x = {-1.391852698, 1.391852698}Subproblem 2
x2 + 6 = -7.937253933 Simplifying x2 + 6 = -7.937253933 Reorder the terms: 6 + x2 = -7.937253933 Solving 6 + x2 = -7.937253933 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 = -7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -7.937253933 + -6 x2 = -7.937253933 + -6 Combine like terms: -7.937253933 + -6 = -13.937253933 x2 = -13.937253933 Simplifying x2 = -13.937253933 Reorder the terms: 13.937253933 + x2 = -13.937253933 + 13.937253933 Combine like terms: -13.937253933 + 13.937253933 = 0.000000000 13.937253933 + 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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