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Simplifying 2x4 + 4x2 + 1 = 0 Reorder the terms: 1 + 4x2 + 2x4 = 0 Solving 1 + 4x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 2x2 + x4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 2x2 + -0.5 + x4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 2x2 + x4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 2x2 + x4 = 0 + -0.5 2x2 + x4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 2x2 + x4 = -0.5 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = -0.5 + 1 Reorder the terms: 1 + 2x2 + x4 = -0.5 + 1 Combine like terms: -0.5 + 1 = 0.5 1 + 2x2 + x4 = 0.5 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x2 + 1) equal to 0.707106781 and -0.707106781.Subproblem 1
x2 + 1 = 0.707106781 Simplifying x2 + 1 = 0.707106781 Reorder the terms: 1 + x2 = 0.707106781 Solving 1 + x2 = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0.707106781 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0.707106781 + -1 x2 = 0.707106781 + -1 Combine like terms: 0.707106781 + -1 = -0.292893219 x2 = -0.292893219 Simplifying x2 = -0.292893219 Reorder the terms: 0.292893219 + x2 = -0.292893219 + 0.292893219 Combine like terms: -0.292893219 + 0.292893219 = 0.000000000 0.292893219 + 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 + 1 = -0.707106781 Simplifying x2 + 1 = -0.707106781 Reorder the terms: 1 + x2 = -0.707106781 Solving 1 + x2 = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -0.707106781 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -0.707106781 + -1 x2 = -0.707106781 + -1 Combine like terms: -0.707106781 + -1 = -1.707106781 x2 = -1.707106781 Simplifying x2 = -1.707106781 Reorder the terms: 1.707106781 + x2 = -1.707106781 + 1.707106781 Combine like terms: -1.707106781 + 1.707106781 = 0.000000000 1.707106781 + 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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