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Simplifying X4 + 12X2 + -8 = 0 Reorder the terms: -8 + 12X2 + X4 = 0 Solving -8 + 12X2 + X4 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 12X2 + 8 + X4 = 0 + 8 Reorder the terms: -8 + 8 + 12X2 + X4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 12X2 + X4 = 0 + 8 12X2 + X4 = 0 + 8 Combine like terms: 0 + 8 = 8 12X2 + X4 = 8 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 = 8 + 36 Reorder the terms: 36 + 12X2 + X4 = 8 + 36 Combine like terms: 8 + 36 = 44 36 + 12X2 + X4 = 44 Factor a perfect square on the left side: (X2 + 6)(X2 + 6) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (X2 + 6) equal to 6.633249581 and -6.633249581.Subproblem 1
X2 + 6 = 6.633249581 Simplifying X2 + 6 = 6.633249581 Reorder the terms: 6 + X2 = 6.633249581 Solving 6 + X2 = 6.633249581 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 = 6.633249581 + -6 Combine like terms: 6 + -6 = 0 0 + X2 = 6.633249581 + -6 X2 = 6.633249581 + -6 Combine like terms: 6.633249581 + -6 = 0.633249581 X2 = 0.633249581 Simplifying X2 = 0.633249581 Take the square root of each side: X = {-0.795769804, 0.795769804}Subproblem 2
X2 + 6 = -6.633249581 Simplifying X2 + 6 = -6.633249581 Reorder the terms: 6 + X2 = -6.633249581 Solving 6 + X2 = -6.633249581 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 = -6.633249581 + -6 Combine like terms: 6 + -6 = 0 0 + X2 = -6.633249581 + -6 X2 = -6.633249581 + -6 Combine like terms: -6.633249581 + -6 = -12.633249581 X2 = -12.633249581 Simplifying X2 = -12.633249581 Reorder the terms: 12.633249581 + X2 = -12.633249581 + 12.633249581 Combine like terms: -12.633249581 + 12.633249581 = 0.000000000 12.633249581 + 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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