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Simplifying 4x4 + 44x2 + 48 = 0 Reorder the terms: 48 + 44x2 + 4x4 = 0 Solving 48 + 44x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 11x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + 11x2 + x4)' equal to zero and attempt to solve: Simplifying 12 + 11x2 + x4 = 0 Solving 12 + 11x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 11x2 + -12 + x4 = 0 + -12 Reorder the terms: 12 + -12 + 11x2 + x4 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 11x2 + x4 = 0 + -12 11x2 + x4 = 0 + -12 Combine like terms: 0 + -12 = -12 11x2 + x4 = -12 The x term is 11x2. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x2 + 30.25 + x4 = -12 + 30.25 Reorder the terms: 30.25 + 11x2 + x4 = -12 + 30.25 Combine like terms: -12 + 30.25 = 18.25 30.25 + 11x2 + x4 = 18.25 Factor a perfect square on the left side: (x2 + 5.5)(x2 + 5.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x2 + 5.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x2 + 5.5 = 4.272001873 Simplifying x2 + 5.5 = 4.272001873 Reorder the terms: 5.5 + x2 = 4.272001873 Solving 5.5 + x2 = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x2 = 4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = 4.272001873 + -5.5 x2 = 4.272001873 + -5.5 Combine like terms: 4.272001873 + -5.5 = -1.227998127 x2 = -1.227998127 Simplifying x2 = -1.227998127 Reorder the terms: 1.227998127 + x2 = -1.227998127 + 1.227998127 Combine like terms: -1.227998127 + 1.227998127 = 0.000000000 1.227998127 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 5.5 = -4.272001873 Simplifying x2 + 5.5 = -4.272001873 Reorder the terms: 5.5 + x2 = -4.272001873 Solving 5.5 + x2 = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x2 = -4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = -4.272001873 + -5.5 x2 = -4.272001873 + -5.5 Combine like terms: -4.272001873 + -5.5 = -9.772001873 x2 = -9.772001873 Simplifying x2 = -9.772001873 Reorder the terms: 9.772001873 + x2 = -9.772001873 + 9.772001873 Combine like terms: -9.772001873 + 9.772001873 = 0.000000000 9.772001873 + x2 = 0.000000000 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. 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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