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Simplifying x4 + -2x2 + -14 = 0 Reorder the terms: -14 + -2x2 + x4 = 0 Solving -14 + -2x2 + 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 + -2x2 + 14 + x4 = 0 + 14 Reorder the terms: -14 + 14 + -2x2 + x4 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2x2 + x4 = 0 + 14 -2x2 + x4 = 0 + 14 Combine like terms: 0 + 14 = 14 -2x2 + x4 = 14 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 14 + 1 Reorder the terms: 1 + -2x2 + x4 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + -2x2 + x4 = 15 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x2 + -1) equal to 3.872983346 and -3.872983346.Subproblem 1
x2 + -1 = 3.872983346 Simplifying x2 + -1 = 3.872983346 Reorder the terms: -1 + x2 = 3.872983346 Solving -1 + x2 = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 3.872983346 + 1 x2 = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 x2 = 4.872983346 Simplifying x2 = 4.872983346 Take the square root of each side: x = {-2.207483487, 2.207483487}Subproblem 2
x2 + -1 = -3.872983346 Simplifying x2 + -1 = -3.872983346 Reorder the terms: -1 + x2 = -3.872983346 Solving -1 + x2 = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -3.872983346 + 1 x2 = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 x2 = -2.872983346 Simplifying x2 = -2.872983346 Reorder the terms: 2.872983346 + x2 = -2.872983346 + 2.872983346 Combine like terms: -2.872983346 + 2.872983346 = 0.000000000 2.872983346 + 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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