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Simplifying x4 + -5x2 + -5 = 0 Reorder the terms: -5 + -5x2 + x4 = 0 Solving -5 + -5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -5x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + -5x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5x2 + x4 = 0 + 5 -5x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 -5x2 + x4 = 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 = 5 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = 5 + 6.25 Combine like terms: 5 + 6.25 = 11.25 6.25 + -5x2 + x4 = 11.25 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x2 + -2.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x2 + -2.5 = 3.354101966 Simplifying x2 + -2.5 = 3.354101966 Reorder the terms: -2.5 + x2 = 3.354101966 Solving -2.5 + x2 = 3.354101966 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 = 3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 3.354101966 + 2.5 x2 = 3.354101966 + 2.5 Combine like terms: 3.354101966 + 2.5 = 5.854101966 x2 = 5.854101966 Simplifying x2 = 5.854101966 Take the square root of each side: x = {-2.419525153, 2.419525153}Subproblem 2
x2 + -2.5 = -3.354101966 Simplifying x2 + -2.5 = -3.354101966 Reorder the terms: -2.5 + x2 = -3.354101966 Solving -2.5 + x2 = -3.354101966 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 = -3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -3.354101966 + 2.5 x2 = -3.354101966 + 2.5 Combine like terms: -3.354101966 + 2.5 = -0.854101966 x2 = -0.854101966 Simplifying x2 = -0.854101966 Reorder the terms: 0.854101966 + x2 = -0.854101966 + 0.854101966 Combine like terms: -0.854101966 + 0.854101966 = 0.000000000 0.854101966 + 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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