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Simplifying x4 + 18x2 + -32 = 0 Reorder the terms: -32 + 18x2 + x4 = 0 Solving -32 + 18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 18x2 + 32 + x4 = 0 + 32 Reorder the terms: -32 + 32 + 18x2 + x4 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 18x2 + x4 = 0 + 32 18x2 + x4 = 0 + 32 Combine like terms: 0 + 32 = 32 18x2 + x4 = 32 The x term is 18x2. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x2 + 81 + x4 = 32 + 81 Reorder the terms: 81 + 18x2 + x4 = 32 + 81 Combine like terms: 32 + 81 = 113 81 + 18x2 + x4 = 113 Factor a perfect square on the left side: (x2 + 9)(x2 + 9) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x2 + 9) equal to 10.630145813 and -10.630145813.Subproblem 1
x2 + 9 = 10.630145813 Simplifying x2 + 9 = 10.630145813 Reorder the terms: 9 + x2 = 10.630145813 Solving 9 + x2 = 10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x2 = 10.630145813 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = 10.630145813 + -9 x2 = 10.630145813 + -9 Combine like terms: 10.630145813 + -9 = 1.630145813 x2 = 1.630145813 Simplifying x2 = 1.630145813 Take the square root of each side: x = {-1.276771637, 1.276771637}Subproblem 2
x2 + 9 = -10.630145813 Simplifying x2 + 9 = -10.630145813 Reorder the terms: 9 + x2 = -10.630145813 Solving 9 + x2 = -10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x2 = -10.630145813 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = -10.630145813 + -9 x2 = -10.630145813 + -9 Combine like terms: -10.630145813 + -9 = -19.630145813 x2 = -19.630145813 Simplifying x2 = -19.630145813 Reorder the terms: 19.630145813 + x2 = -19.630145813 + 19.630145813 Combine like terms: -19.630145813 + 19.630145813 = 0.000000000 19.630145813 + 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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