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Simplifying 16 + 48x2 + 2x4 = 136 Solving 16 + 48x2 + 2x4 = 136 Solving for variable 'x'. Reorder the terms: 16 + -136 + 48x2 + 2x4 = 136 + -136 Combine like terms: 16 + -136 = -120 -120 + 48x2 + 2x4 = 136 + -136 Combine like terms: 136 + -136 = 0 -120 + 48x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 24x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 24x2 + x4)' equal to zero and attempt to solve: Simplifying -60 + 24x2 + x4 = 0 Solving -60 + 24x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 24x2 + 60 + x4 = 0 + 60 Reorder the terms: -60 + 60 + 24x2 + x4 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 24x2 + x4 = 0 + 60 24x2 + x4 = 0 + 60 Combine like terms: 0 + 60 = 60 24x2 + x4 = 60 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 = 60 + 144 Reorder the terms: 144 + 24x2 + x4 = 60 + 144 Combine like terms: 60 + 144 = 204 144 + 24x2 + x4 = 204 Factor a perfect square on the left side: (x2 + 12)(x2 + 12) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x2 + 12) equal to 14.282856857 and -14.282856857.Subproblem 1
x2 + 12 = 14.282856857 Simplifying x2 + 12 = 14.282856857 Reorder the terms: 12 + x2 = 14.282856857 Solving 12 + x2 = 14.282856857 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 = 14.282856857 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = 14.282856857 + -12 x2 = 14.282856857 + -12 Combine like terms: 14.282856857 + -12 = 2.282856857 x2 = 2.282856857 Simplifying x2 = 2.282856857 Take the square root of each side: x = {-1.510912591, 1.510912591}Subproblem 2
x2 + 12 = -14.282856857 Simplifying x2 + 12 = -14.282856857 Reorder the terms: 12 + x2 = -14.282856857 Solving 12 + x2 = -14.282856857 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 = -14.282856857 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = -14.282856857 + -12 x2 = -14.282856857 + -12 Combine like terms: -14.282856857 + -12 = -26.282856857 x2 = -26.282856857 Simplifying x2 = -26.282856857 Reorder the terms: 26.282856857 + x2 = -26.282856857 + 26.282856857 Combine like terms: -26.282856857 + 26.282856857 = 0.000000000 26.282856857 + 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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