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Simplifying x4 + -6x2 + -14 = 0 Reorder the terms: -14 + -6x2 + x4 = 0 Solving -14 + -6x2 + 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 + -6x2 + 14 + x4 = 0 + 14 Reorder the terms: -14 + 14 + -6x2 + x4 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -6x2 + x4 = 0 + 14 -6x2 + x4 = 0 + 14 Combine like terms: 0 + 14 = 14 -6x2 + x4 = 14 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = 14 + 9 Reorder the terms: 9 + -6x2 + x4 = 14 + 9 Combine like terms: 14 + 9 = 23 9 + -6x2 + x4 = 23 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x2 + -3) equal to 4.795831523 and -4.795831523.Subproblem 1
x2 + -3 = 4.795831523 Simplifying x2 + -3 = 4.795831523 Reorder the terms: -3 + x2 = 4.795831523 Solving -3 + x2 = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 4.795831523 + 3 x2 = 4.795831523 + 3 Combine like terms: 4.795831523 + 3 = 7.795831523 x2 = 7.795831523 Simplifying x2 = 7.795831523 Take the square root of each side: x = {-2.792101632, 2.792101632}Subproblem 2
x2 + -3 = -4.795831523 Simplifying x2 + -3 = -4.795831523 Reorder the terms: -3 + x2 = -4.795831523 Solving -3 + x2 = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -4.795831523 + 3 x2 = -4.795831523 + 3 Combine like terms: -4.795831523 + 3 = -1.795831523 x2 = -1.795831523 Simplifying x2 = -1.795831523 Reorder the terms: 1.795831523 + x2 = -1.795831523 + 1.795831523 Combine like terms: -1.795831523 + 1.795831523 = 0.000000000 1.795831523 + 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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