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Simplifying x4 + x2 + -144 = 0 Reorder the terms: -144 + x2 + x4 = 0 Solving -144 + x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + x2 + 144 + x4 = 0 + 144 Reorder the terms: -144 + 144 + x2 + x4 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + x2 + x4 = 0 + 144 x2 + x4 = 0 + 144 Combine like terms: 0 + 144 = 144 x2 + x4 = 144 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x2 + 0.25 + x4 = 144 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 144 + 0.25 Combine like terms: 144 + 0.25 = 144.25 0.25 + x2 + x4 = 144.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x2 + 0.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x2 + 0.5 = 12.010412149 Simplifying x2 + 0.5 = 12.010412149 Reorder the terms: 0.5 + x2 = 12.010412149 Solving 0.5 + x2 = 12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 12.010412149 + -0.5 x2 = 12.010412149 + -0.5 Combine like terms: 12.010412149 + -0.5 = 11.510412149 x2 = 11.510412149 Simplifying x2 = 11.510412149 Take the square root of each side: x = {-3.392699832, 3.392699832}Subproblem 2
x2 + 0.5 = -12.010412149 Simplifying x2 + 0.5 = -12.010412149 Reorder the terms: 0.5 + x2 = -12.010412149 Solving 0.5 + x2 = -12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -12.010412149 + -0.5 x2 = -12.010412149 + -0.5 Combine like terms: -12.010412149 + -0.5 = -12.510412149 x2 = -12.510412149 Simplifying x2 = -12.510412149 Reorder the terms: 12.510412149 + x2 = -12.510412149 + 12.510412149 Combine like terms: -12.510412149 + 12.510412149 = 0.000000000 12.510412149 + 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.
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