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Simplifying 4x4 + 2x2 + 20 = 0 Reorder the terms: 20 + 2x2 + 4x4 = 0 Solving 20 + 2x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + x2 + 2x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + x2 + 2x4)' equal to zero and attempt to solve: Simplifying 10 + x2 + 2x4 = 0 Solving 10 + x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 0.5x2 + -5 + x4 = 0 + -5 Reorder the terms: 5 + -5 + 0.5x2 + x4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 0.5x2 + x4 = 0 + -5 0.5x2 + x4 = 0 + -5 Combine like terms: 0 + -5 = -5 0.5x2 + x4 = -5 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x2 + 0.25 + x4 = -5 + 0.25 Reorder the terms: 0.25 + 0.5x2 + x4 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + 0.5x2 + x4 = -4.75 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = -4.75 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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