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Simplifying x4 + 8x2 + 6 = 0 Reorder the terms: 6 + 8x2 + x4 = 0 Solving 6 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 8x2 + -6 + x4 = 0 + -6 Reorder the terms: 6 + -6 + 8x2 + x4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 8x2 + x4 = 0 + -6 8x2 + x4 = 0 + -6 Combine like terms: 0 + -6 = -6 8x2 + x4 = -6 The x term is 8x2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x2 + 16 + x4 = -6 + 16 Reorder the terms: 16 + 8x2 + x4 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + 8x2 + x4 = 10 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x2 + 4) equal to 3.16227766 and -3.16227766.Subproblem 1
x2 + 4 = 3.16227766 Simplifying x2 + 4 = 3.16227766 Reorder the terms: 4 + x2 = 3.16227766 Solving 4 + x2 = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 3.16227766 + -4 x2 = 3.16227766 + -4 Combine like terms: 3.16227766 + -4 = -0.83772234 x2 = -0.83772234 Simplifying x2 = -0.83772234 Reorder the terms: 0.83772234 + x2 = -0.83772234 + 0.83772234 Combine like terms: -0.83772234 + 0.83772234 = 0.00000000 0.83772234 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 4 = -3.16227766 Simplifying x2 + 4 = -3.16227766 Reorder the terms: 4 + x2 = -3.16227766 Solving 4 + x2 = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -3.16227766 + -4 x2 = -3.16227766 + -4 Combine like terms: -3.16227766 + -4 = -7.16227766 x2 = -7.16227766 Simplifying x2 = -7.16227766 Reorder the terms: 7.16227766 + x2 = -7.16227766 + 7.16227766 Combine like terms: -7.16227766 + 7.16227766 = 0.00000000 7.16227766 + 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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