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Simplifying x4 + 10x2 + -14 = 0 Reorder the terms: -14 + 10x2 + x4 = 0 Solving -14 + 10x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 10x2 + 14 + x4 = 0 + 14 Reorder the terms: -14 + 14 + 10x2 + x4 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 10x2 + x4 = 0 + 14 10x2 + x4 = 0 + 14 Combine like terms: 0 + 14 = 14 10x2 + x4 = 14 The x term is 10x2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x2 + 25 + x4 = 14 + 25 Reorder the terms: 25 + 10x2 + x4 = 14 + 25 Combine like terms: 14 + 25 = 39 25 + 10x2 + x4 = 39 Factor a perfect square on the left side: (x2 + 5)(x2 + 5) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x2 + 5) equal to 6.244997998 and -6.244997998.Subproblem 1
x2 + 5 = 6.244997998 Simplifying x2 + 5 = 6.244997998 Reorder the terms: 5 + x2 = 6.244997998 Solving 5 + x2 = 6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 6.244997998 + -5 x2 = 6.244997998 + -5 Combine like terms: 6.244997998 + -5 = 1.244997998 x2 = 1.244997998 Simplifying x2 = 1.244997998 Take the square root of each side: x = {-1.115794783, 1.115794783}Subproblem 2
x2 + 5 = -6.244997998 Simplifying x2 + 5 = -6.244997998 Reorder the terms: 5 + x2 = -6.244997998 Solving 5 + x2 = -6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = -6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = -6.244997998 + -5 x2 = -6.244997998 + -5 Combine like terms: -6.244997998 + -5 = -11.244997998 x2 = -11.244997998 Simplifying x2 = -11.244997998 Reorder the terms: 11.244997998 + x2 = -11.244997998 + 11.244997998 Combine like terms: -11.244997998 + 11.244997998 = 0.000000000 11.244997998 + 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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