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Simplifying x4 + -108x2 + -729 = 0 Reorder the terms: -729 + -108x2 + x4 = 0 Solving -729 + -108x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '729' to each side of the equation. -729 + -108x2 + 729 + x4 = 0 + 729 Reorder the terms: -729 + 729 + -108x2 + x4 = 0 + 729 Combine like terms: -729 + 729 = 0 0 + -108x2 + x4 = 0 + 729 -108x2 + x4 = 0 + 729 Combine like terms: 0 + 729 = 729 -108x2 + x4 = 729 The x term is -108x2. Take half its coefficient (-54). Square it (2916) and add it to both sides. Add '2916' to each side of the equation. -108x2 + 2916 + x4 = 729 + 2916 Reorder the terms: 2916 + -108x2 + x4 = 729 + 2916 Combine like terms: 729 + 2916 = 3645 2916 + -108x2 + x4 = 3645 Factor a perfect square on the left side: (x2 + -54)(x2 + -54) = 3645 Calculate the square root of the right side: 60.373835392 Break this problem into two subproblems by setting (x2 + -54) equal to 60.373835392 and -60.373835392.Subproblem 1
x2 + -54 = 60.373835392 Simplifying x2 + -54 = 60.373835392 Reorder the terms: -54 + x2 = 60.373835392 Solving -54 + x2 = 60.373835392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + x2 = 60.373835392 + 54 Combine like terms: -54 + 54 = 0 0 + x2 = 60.373835392 + 54 x2 = 60.373835392 + 54 Combine like terms: 60.373835392 + 54 = 114.373835392 x2 = 114.373835392 Simplifying x2 = 114.373835392 Take the square root of each side: x = {-10.69457037, 10.69457037}Subproblem 2
x2 + -54 = -60.373835392 Simplifying x2 + -54 = -60.373835392 Reorder the terms: -54 + x2 = -60.373835392 Solving -54 + x2 = -60.373835392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + x2 = -60.373835392 + 54 Combine like terms: -54 + 54 = 0 0 + x2 = -60.373835392 + 54 x2 = -60.373835392 + 54 Combine like terms: -60.373835392 + 54 = -6.373835392 x2 = -6.373835392 Simplifying x2 = -6.373835392 Reorder the terms: 6.373835392 + x2 = -6.373835392 + 6.373835392 Combine like terms: -6.373835392 + 6.373835392 = 0.000000000 6.373835392 + 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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