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Simplifying 6x4 + 8x2 + 54 = 0 Reorder the terms: 54 + 8x2 + 6x4 = 0 Solving 54 + 8x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 4x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + 4x2 + 3x4)' equal to zero and attempt to solve: Simplifying 27 + 4x2 + 3x4 = 0 Solving 27 + 4x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9 + 1.333333333x2 + x4 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 1.333333333x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + 1.333333333x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 1.333333333x2 + x4 = 0 + -9 1.333333333x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 1.333333333x2 + x4 = -9 The x term is 1.333333333x2. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x2 + 0.4444444442 + x4 = -9 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x2 + x4 = -9 + 0.4444444442 Combine like terms: -9 + 0.4444444442 = -8.5555555558 0.4444444442 + 1.333333333x2 + x4 = -8.5555555558 Factor a perfect square on the left side: (x2 + 0.6666666665)(x2 + 0.6666666665) = -8.5555555558 Can't calculate square root of the right side. 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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