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Simplifying x4 + 8x2 = 1 Reorder the terms: 8x2 + x4 = 1 Solving 8x2 + x4 = 1 Solving for variable 'x'. Reorder the terms: -1 + 8x2 + x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 8x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + 8x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8x2 + x4 = 0 + 1 8x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 8x2 + x4 = 1 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 = 1 + 16 Reorder the terms: 16 + 8x2 + x4 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + 8x2 + x4 = 17 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x2 + 4) equal to 4.123105626 and -4.123105626.Subproblem 1
x2 + 4 = 4.123105626 Simplifying x2 + 4 = 4.123105626 Reorder the terms: 4 + x2 = 4.123105626 Solving 4 + x2 = 4.123105626 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 = 4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 4.123105626 + -4 x2 = 4.123105626 + -4 Combine like terms: 4.123105626 + -4 = 0.123105626 x2 = 0.123105626 Simplifying x2 = 0.123105626 Take the square root of each side: x = {-0.350864113, 0.350864113}Subproblem 2
x2 + 4 = -4.123105626 Simplifying x2 + 4 = -4.123105626 Reorder the terms: 4 + x2 = -4.123105626 Solving 4 + x2 = -4.123105626 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 = -4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -4.123105626 + -4 x2 = -4.123105626 + -4 Combine like terms: -4.123105626 + -4 = -8.123105626 x2 = -8.123105626 Simplifying x2 = -8.123105626 Reorder the terms: 8.123105626 + x2 = -8.123105626 + 8.123105626 Combine like terms: -8.123105626 + 8.123105626 = 0.000000000 8.123105626 + 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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