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Simplifying -4x2 + -1x4 + -5 = 0 Reorder the terms: -5 + -4x2 + -1x4 = 0 Solving -5 + -4x2 + -1x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 4x2 + x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying 5 + 4x2 + x4 = 0 Solving 5 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4x2 + -5 + x4 = 0 + -5 Reorder the terms: 5 + -5 + 4x2 + x4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x2 + x4 = 0 + -5 4x2 + x4 = 0 + -5 Combine like terms: 0 + -5 = -5 4x2 + x4 = -5 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = -5 + 4 Reorder the terms: 4 + 4x2 + x4 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + 4x2 + x4 = -1 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = -1 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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