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Simplifying x4 + 6x2 + 4 = 0 Reorder the terms: 4 + 6x2 + x4 = 0 Solving 4 + 6x2 + 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 + 6x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + 6x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6x2 + x4 = 0 + -4 6x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 6x2 + x4 = -4 The x term is 6x2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x2 + 9 + x4 = -4 + 9 Reorder the terms: 9 + 6x2 + x4 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + 6x2 + x4 = 5 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x2 + 3) equal to 2.236067978 and -2.236067978.Subproblem 1
x2 + 3 = 2.236067978 Simplifying x2 + 3 = 2.236067978 Reorder the terms: 3 + x2 = 2.236067978 Solving 3 + x2 = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 2.236067978 + -3 x2 = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 x2 = -0.763932022 Simplifying x2 = -0.763932022 Reorder the terms: 0.763932022 + x2 = -0.763932022 + 0.763932022 Combine like terms: -0.763932022 + 0.763932022 = 0.000000000 0.763932022 + 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 + 3 = -2.236067978 Simplifying x2 + 3 = -2.236067978 Reorder the terms: 3 + x2 = -2.236067978 Solving 3 + x2 = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -2.236067978 + -3 x2 = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 x2 = -5.236067978 Simplifying x2 = -5.236067978 Reorder the terms: 5.236067978 + x2 = -5.236067978 + 5.236067978 Combine like terms: -5.236067978 + 5.236067978 = 0.000000000 5.236067978 + 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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