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Simplifying 2x4 + 48x2 + 168 = 0 Reorder the terms: 168 + 48x2 + 2x4 = 0 Solving 168 + 48x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(84 + 24x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(84 + 24x2 + x4)' equal to zero and attempt to solve: Simplifying 84 + 24x2 + x4 = 0 Solving 84 + 24x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 24x2 + -84 + x4 = 0 + -84 Reorder the terms: 84 + -84 + 24x2 + x4 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 24x2 + x4 = 0 + -84 24x2 + x4 = 0 + -84 Combine like terms: 0 + -84 = -84 24x2 + x4 = -84 The x term is 24x2. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x2 + 144 + x4 = -84 + 144 Reorder the terms: 144 + 24x2 + x4 = -84 + 144 Combine like terms: -84 + 144 = 60 144 + 24x2 + x4 = 60 Factor a perfect square on the left side: (x2 + 12)(x2 + 12) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x2 + 12) equal to 7.745966692 and -7.745966692.Subproblem 1
x2 + 12 = 7.745966692 Simplifying x2 + 12 = 7.745966692 Reorder the terms: 12 + x2 = 7.745966692 Solving 12 + x2 = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = 7.745966692 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = 7.745966692 + -12 x2 = 7.745966692 + -12 Combine like terms: 7.745966692 + -12 = -4.254033308 x2 = -4.254033308 Simplifying x2 = -4.254033308 Reorder the terms: 4.254033308 + x2 = -4.254033308 + 4.254033308 Combine like terms: -4.254033308 + 4.254033308 = 0.000000000 4.254033308 + 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 + 12 = -7.745966692 Simplifying x2 + 12 = -7.745966692 Reorder the terms: 12 + x2 = -7.745966692 Solving 12 + x2 = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = -7.745966692 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = -7.745966692 + -12 x2 = -7.745966692 + -12 Combine like terms: -7.745966692 + -12 = -19.745966692 x2 = -19.745966692 Simplifying x2 = -19.745966692 Reorder the terms: 19.745966692 + x2 = -19.745966692 + 19.745966692 Combine like terms: -19.745966692 + 19.745966692 = 0.000000000 19.745966692 + 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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