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Simplifying 4x4 + 8x2 + 140 = 0 Reorder the terms: 140 + 8x2 + 4x4 = 0 Solving 140 + 8x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(35 + 2x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + 2x2 + x4)' equal to zero and attempt to solve: Simplifying 35 + 2x2 + x4 = 0 Solving 35 + 2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 2x2 + -35 + x4 = 0 + -35 Reorder the terms: 35 + -35 + 2x2 + x4 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 2x2 + x4 = 0 + -35 2x2 + x4 = 0 + -35 Combine like terms: 0 + -35 = -35 2x2 + x4 = -35 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 = -35 + 1 Reorder the terms: 1 + 2x2 + x4 = -35 + 1 Combine like terms: -35 + 1 = -34 1 + 2x2 + x4 = -34 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = -34 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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