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Simplifying 2x4 + 6x2 + 6 = 0 Reorder the terms: 6 + 6x2 + 2x4 = 0 Solving 6 + 6x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 3x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 3x2 + x4)' equal to zero and attempt to solve: Simplifying 3 + 3x2 + x4 = 0 Solving 3 + 3x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3x2 + -3 + x4 = 0 + -3 Reorder the terms: 3 + -3 + 3x2 + x4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3x2 + x4 = 0 + -3 3x2 + x4 = 0 + -3 Combine like terms: 0 + -3 = -3 3x2 + x4 = -3 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = -3 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = -3 + 2.25 Combine like terms: -3 + 2.25 = -0.75 2.25 + 3x2 + x4 = -0.75 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = -0.75 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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