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Simplifying x4 + -4x2 = 2 Reorder the terms: -4x2 + x4 = 2 Solving -4x2 + x4 = 2 Solving for variable 'x'. Reorder the terms: -2 + -4x2 + x4 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + -4x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4x2 + x4 = 0 + 2 -4x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 -4x2 + x4 = 2 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 = 2 + 4 Reorder the terms: 4 + -4x2 + x4 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4x2 + x4 = 6 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + -2 = 2.449489743 Simplifying x2 + -2 = 2.449489743 Reorder the terms: -2 + x2 = 2.449489743 Solving -2 + x2 = 2.449489743 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 = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.449489743 + 2 x2 = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 x2 = 4.449489743 Simplifying x2 = 4.449489743 Take the square root of each side: x = {-2.109381365, 2.109381365}Subproblem 2
x2 + -2 = -2.449489743 Simplifying x2 + -2 = -2.449489743 Reorder the terms: -2 + x2 = -2.449489743 Solving -2 + x2 = -2.449489743 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 = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.449489743 + 2 x2 = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 x2 = -0.449489743 Simplifying x2 = -0.449489743 Reorder the terms: 0.449489743 + x2 = -0.449489743 + 0.449489743 Combine like terms: -0.449489743 + 0.449489743 = 0.000000000 0.449489743 + 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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