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Simplifying x4 + 4x2 = 1 Reorder the terms: 4x2 + x4 = 1 Solving 4x2 + x4 = 1 Solving for variable 'x'. Reorder the terms: -1 + 4x2 + x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 4x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + 4x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x2 + x4 = 0 + 1 4x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 4x2 + x4 = 1 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 1 + 4 Reorder the terms: 4 + 4x2 + x4 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4x2 + x4 = 5 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x2 + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
x2 + 2 = 2.236067978 Simplifying x2 + 2 = 2.236067978 Reorder the terms: 2 + x2 = 2.236067978 Solving 2 + x2 = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 2.236067978 + -2 x2 = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 x2 = 0.236067978 Simplifying x2 = 0.236067978 Take the square root of each side: x = {-0.485868272, 0.485868272}Subproblem 2
x2 + 2 = -2.236067978 Simplifying x2 + 2 = -2.236067978 Reorder the terms: 2 + x2 = -2.236067978 Solving 2 + x2 = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -2.236067978 + -2 x2 = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 x2 = -4.236067978 Simplifying x2 = -4.236067978 Reorder the terms: 4.236067978 + x2 = -4.236067978 + 4.236067978 Combine like terms: -4.236067978 + 4.236067978 = 0.000000000 4.236067978 + 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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