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Simplifying x4 + x2 = 684 Reorder the terms: x2 + x4 = 684 Solving x2 + x4 = 684 Solving for variable 'x'. Reorder the terms: -684 + x2 + x4 = 684 + -684 Combine like terms: 684 + -684 = 0 -684 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '684' to each side of the equation. -684 + x2 + 684 + x4 = 0 + 684 Reorder the terms: -684 + 684 + x2 + x4 = 0 + 684 Combine like terms: -684 + 684 = 0 0 + x2 + x4 = 0 + 684 x2 + x4 = 0 + 684 Combine like terms: 0 + 684 = 684 x2 + x4 = 684 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 = 684 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 684 + 0.25 Combine like terms: 684 + 0.25 = 684.25 0.25 + x2 + x4 = 684.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 684.25 Calculate the square root of the right side: 26.158172719 Break this problem into two subproblems by setting (x2 + 0.5) equal to 26.158172719 and -26.158172719.Subproblem 1
x2 + 0.5 = 26.158172719 Simplifying x2 + 0.5 = 26.158172719 Reorder the terms: 0.5 + x2 = 26.158172719 Solving 0.5 + x2 = 26.158172719 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 = 26.158172719 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 26.158172719 + -0.5 x2 = 26.158172719 + -0.5 Combine like terms: 26.158172719 + -0.5 = 25.658172719 x2 = 25.658172719 Simplifying x2 = 25.658172719 Take the square root of each side: x = {-5.065389691, 5.065389691}Subproblem 2
x2 + 0.5 = -26.158172719 Simplifying x2 + 0.5 = -26.158172719 Reorder the terms: 0.5 + x2 = -26.158172719 Solving 0.5 + x2 = -26.158172719 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 = -26.158172719 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -26.158172719 + -0.5 x2 = -26.158172719 + -0.5 Combine like terms: -26.158172719 + -0.5 = -26.658172719 x2 = -26.658172719 Simplifying x2 = -26.658172719 Reorder the terms: 26.658172719 + x2 = -26.658172719 + 26.658172719 Combine like terms: -26.658172719 + 26.658172719 = 0.000000000 26.658172719 + 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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