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Simplifying 3x4 + 6x2 + 1 = 0 Reorder the terms: 1 + 6x2 + 3x4 = 0 Solving 1 + 6x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 2x2 + x4 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 2x2 + -0.3333333333 + x4 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 2x2 + x4 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 2x2 + x4 = 0 + -0.3333333333 2x2 + x4 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 2x2 + x4 = -0.3333333333 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 = -0.3333333333 + 1 Reorder the terms: 1 + 2x2 + x4 = -0.3333333333 + 1 Combine like terms: -0.3333333333 + 1 = 0.6666666667 1 + 2x2 + x4 = 0.6666666667 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 0.6666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x2 + 1) equal to 0.816496581 and -0.816496581.Subproblem 1
x2 + 1 = 0.816496581 Simplifying x2 + 1 = 0.816496581 Reorder the terms: 1 + x2 = 0.816496581 Solving 1 + x2 = 0.816496581 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 = 0.816496581 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0.816496581 + -1 x2 = 0.816496581 + -1 Combine like terms: 0.816496581 + -1 = -0.183503419 x2 = -0.183503419 Simplifying x2 = -0.183503419 Reorder the terms: 0.183503419 + x2 = -0.183503419 + 0.183503419 Combine like terms: -0.183503419 + 0.183503419 = 0.000000000 0.183503419 + 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 = -0.816496581 Simplifying x2 + 1 = -0.816496581 Reorder the terms: 1 + x2 = -0.816496581 Solving 1 + x2 = -0.816496581 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 = -0.816496581 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -0.816496581 + -1 x2 = -0.816496581 + -1 Combine like terms: -0.816496581 + -1 = -1.816496581 x2 = -1.816496581 Simplifying x2 = -1.816496581 Reorder the terms: 1.816496581 + x2 = -1.816496581 + 1.816496581 Combine like terms: -1.816496581 + 1.816496581 = 0.000000000 1.816496581 + 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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