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Simplifying 6x4 + 12x2 + 120 = 0 Reorder the terms: 120 + 12x2 + 6x4 = 0 Solving 120 + 12x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(20 + 2x2 + x4) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(20 + 2x2 + x4)' equal to zero and attempt to solve: Simplifying 20 + 2x2 + x4 = 0 Solving 20 + 2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 2x2 + -20 + x4 = 0 + -20 Reorder the terms: 20 + -20 + 2x2 + x4 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 2x2 + x4 = 0 + -20 2x2 + x4 = 0 + -20 Combine like terms: 0 + -20 = -20 2x2 + x4 = -20 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = -20 + 1 Reorder the terms: 1 + 2x2 + x4 = -20 + 1 Combine like terms: -20 + 1 = -19 1 + 2x2 + x4 = -19 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = -19 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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