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Simplifying x4 + 18x2 + 8 = 0 Reorder the terms: 8 + 18x2 + x4 = 0 Solving 8 + 18x2 + 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 + 18x2 + -8 + x4 = 0 + -8 Reorder the terms: 8 + -8 + 18x2 + x4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 18x2 + x4 = 0 + -8 18x2 + x4 = 0 + -8 Combine like terms: 0 + -8 = -8 18x2 + x4 = -8 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 = -8 + 81 Reorder the terms: 81 + 18x2 + x4 = -8 + 81 Combine like terms: -8 + 81 = 73 81 + 18x2 + x4 = 73 Factor a perfect square on the left side: (x2 + 9)(x2 + 9) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x2 + 9) equal to 8.544003745 and -8.544003745.Subproblem 1
x2 + 9 = 8.544003745 Simplifying x2 + 9 = 8.544003745 Reorder the terms: 9 + x2 = 8.544003745 Solving 9 + x2 = 8.544003745 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 = 8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = 8.544003745 + -9 x2 = 8.544003745 + -9 Combine like terms: 8.544003745 + -9 = -0.455996255 x2 = -0.455996255 Simplifying x2 = -0.455996255 Reorder the terms: 0.455996255 + x2 = -0.455996255 + 0.455996255 Combine like terms: -0.455996255 + 0.455996255 = 0.000000000 0.455996255 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 9 = -8.544003745 Simplifying x2 + 9 = -8.544003745 Reorder the terms: 9 + x2 = -8.544003745 Solving 9 + x2 = -8.544003745 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 = -8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = -8.544003745 + -9 x2 = -8.544003745 + -9 Combine like terms: -8.544003745 + -9 = -17.544003745 x2 = -17.544003745 Simplifying x2 = -17.544003745 Reorder the terms: 17.544003745 + x2 = -17.544003745 + 17.544003745 Combine like terms: -17.544003745 + 17.544003745 = 0.000000000 17.544003745 + 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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