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Simplifying x4 + 12x2 + -12 = 0 Reorder the terms: -12 + 12x2 + x4 = 0 Solving -12 + 12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 12x2 + 12 + x4 = 0 + 12 Reorder the terms: -12 + 12 + 12x2 + x4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 12x2 + x4 = 0 + 12 12x2 + x4 = 0 + 12 Combine like terms: 0 + 12 = 12 12x2 + x4 = 12 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 = 12 + 36 Reorder the terms: 36 + 12x2 + x4 = 12 + 36 Combine like terms: 12 + 36 = 48 36 + 12x2 + x4 = 48 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x2 + 6) equal to 6.92820323 and -6.92820323.Subproblem 1
x2 + 6 = 6.92820323 Simplifying x2 + 6 = 6.92820323 Reorder the terms: 6 + x2 = 6.92820323 Solving 6 + x2 = 6.92820323 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 = 6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 6.92820323 + -6 x2 = 6.92820323 + -6 Combine like terms: 6.92820323 + -6 = 0.92820323 x2 = 0.92820323 Simplifying x2 = 0.92820323 Take the square root of each side: x = {-0.963433044, 0.963433044}Subproblem 2
x2 + 6 = -6.92820323 Simplifying x2 + 6 = -6.92820323 Reorder the terms: 6 + x2 = -6.92820323 Solving 6 + x2 = -6.92820323 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 = -6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -6.92820323 + -6 x2 = -6.92820323 + -6 Combine like terms: -6.92820323 + -6 = -12.92820323 x2 = -12.92820323 Simplifying x2 = -12.92820323 Reorder the terms: 12.92820323 + x2 = -12.92820323 + 12.92820323 Combine like terms: -12.92820323 + 12.92820323 = 0.00000000 12.92820323 + 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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