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Simplifying x4 + -5x2 + -0.5 = 0 Reorder the terms: -0.5 + -5x2 + x4 = 0 Solving -0.5 + -5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5x2 + x4 = 0 + 0.5 -5x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5x2 + x4 = 0.5 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = 0.5 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = 0.5 + 6.25 Combine like terms: 0.5 + 6.25 = 6.75 6.25 + -5x2 + x4 = 6.75 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x2 + -2.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x2 + -2.5 = 2.598076211 Simplifying x2 + -2.5 = 2.598076211 Reorder the terms: -2.5 + x2 = 2.598076211 Solving -2.5 + x2 = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 2.598076211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 2.598076211 + 2.5 x2 = 2.598076211 + 2.5 Combine like terms: 2.598076211 + 2.5 = 5.098076211 x2 = 5.098076211 Simplifying x2 = 5.098076211 Take the square root of each side: x = {-2.257891984, 2.257891984}Subproblem 2
x2 + -2.5 = -2.598076211 Simplifying x2 + -2.5 = -2.598076211 Reorder the terms: -2.5 + x2 = -2.598076211 Solving -2.5 + x2 = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -2.598076211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -2.598076211 + 2.5 x2 = -2.598076211 + 2.5 Combine like terms: -2.598076211 + 2.5 = -0.098076211 x2 = -0.098076211 Simplifying x2 = -0.098076211 Reorder the terms: 0.098076211 + x2 = -0.098076211 + 0.098076211 Combine like terms: -0.098076211 + 0.098076211 = 0.000000000 0.098076211 + 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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