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Simplifying x4 + x2 = 4 Reorder the terms: x2 + x4 = 4 Solving x2 + x4 = 4 Solving for variable 'x'. Reorder the terms: -4 + x2 + x4 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x2 + x4 = 0 + 4 x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 x2 + x4 = 4 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x2 + 0.25 + x4 = 4 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + x2 + x4 = 4.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x2 + 0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x2 + 0.5 = 2.061552813 Simplifying x2 + 0.5 = 2.061552813 Reorder the terms: 0.5 + x2 = 2.061552813 Solving 0.5 + x2 = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 2.061552813 + -0.5 x2 = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 x2 = 1.561552813 Simplifying x2 = 1.561552813 Take the square root of each side: x = {-1.249621068, 1.249621068}Subproblem 2
x2 + 0.5 = -2.061552813 Simplifying x2 + 0.5 = -2.061552813 Reorder the terms: 0.5 + x2 = -2.061552813 Solving 0.5 + x2 = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -2.061552813 + -0.5 x2 = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 x2 = -2.561552813 Simplifying x2 = -2.561552813 Reorder the terms: 2.561552813 + x2 = -2.561552813 + 2.561552813 Combine like terms: -2.561552813 + 2.561552813 = 0.000000000 2.561552813 + 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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