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Simplifying x4 + 21x2 + 4 = 0 Reorder the terms: 4 + 21x2 + x4 = 0 Solving 4 + 21x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 21x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + 21x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 21x2 + x4 = 0 + -4 21x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 21x2 + x4 = -4 The x term is 21x2. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x2 + 110.25 + x4 = -4 + 110.25 Reorder the terms: 110.25 + 21x2 + x4 = -4 + 110.25 Combine like terms: -4 + 110.25 = 106.25 110.25 + 21x2 + x4 = 106.25 Factor a perfect square on the left side: (x2 + 10.5)(x2 + 10.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x2 + 10.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x2 + 10.5 = 10.307764064 Simplifying x2 + 10.5 = 10.307764064 Reorder the terms: 10.5 + x2 = 10.307764064 Solving 10.5 + x2 = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x2 = 10.307764064 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x2 = 10.307764064 + -10.5 x2 = 10.307764064 + -10.5 Combine like terms: 10.307764064 + -10.5 = -0.192235936 x2 = -0.192235936 Simplifying x2 = -0.192235936 Reorder the terms: 0.192235936 + x2 = -0.192235936 + 0.192235936 Combine like terms: -0.192235936 + 0.192235936 = 0.000000000 0.192235936 + 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 + 10.5 = -10.307764064 Simplifying x2 + 10.5 = -10.307764064 Reorder the terms: 10.5 + x2 = -10.307764064 Solving 10.5 + x2 = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x2 = -10.307764064 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x2 = -10.307764064 + -10.5 x2 = -10.307764064 + -10.5 Combine like terms: -10.307764064 + -10.5 = -20.807764064 x2 = -20.807764064 Simplifying x2 = -20.807764064 Reorder the terms: 20.807764064 + x2 = -20.807764064 + 20.807764064 Combine like terms: -20.807764064 + 20.807764064 = 0.000000000 20.807764064 + 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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