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Simplifying 9x4 + 36x2 + 144 = 0 Reorder the terms: 144 + 36x2 + 9x4 = 0 Solving 144 + 36x2 + 9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(16 + 4x2 + x4) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(16 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying 16 + 4x2 + x4 = 0 Solving 16 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 4x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + 4x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 4x2 + x4 = 0 + -16 4x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 4x2 + x4 = -16 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 = -16 + 4 Reorder the terms: 4 + 4x2 + x4 = -16 + 4 Combine like terms: -16 + 4 = -12 4 + 4x2 + x4 = -12 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = -12 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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