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Simplifying x4 + 7x2 + 8 = 14 Reorder the terms: 8 + 7x2 + x4 = 14 Solving 8 + 7x2 + x4 = 14 Solving for variable 'x'. Reorder the terms: 8 + -14 + 7x2 + x4 = 14 + -14 Combine like terms: 8 + -14 = -6 -6 + 7x2 + x4 = 14 + -14 Combine like terms: 14 + -14 = 0 -6 + 7x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 7x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + 7x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7x2 + x4 = 0 + 6 7x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 7x2 + x4 = 6 The x term is 7x2. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x2 + 12.25 + x4 = 6 + 12.25 Reorder the terms: 12.25 + 7x2 + x4 = 6 + 12.25 Combine like terms: 6 + 12.25 = 18.25 12.25 + 7x2 + x4 = 18.25 Factor a perfect square on the left side: (x2 + 3.5)(x2 + 3.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x2 + 3.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x2 + 3.5 = 4.272001873 Simplifying x2 + 3.5 = 4.272001873 Reorder the terms: 3.5 + x2 = 4.272001873 Solving 3.5 + x2 = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = 4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = 4.272001873 + -3.5 x2 = 4.272001873 + -3.5 Combine like terms: 4.272001873 + -3.5 = 0.772001873 x2 = 0.772001873 Simplifying x2 = 0.772001873 Take the square root of each side: x = {-0.878636371, 0.878636371}Subproblem 2
x2 + 3.5 = -4.272001873 Simplifying x2 + 3.5 = -4.272001873 Reorder the terms: 3.5 + x2 = -4.272001873 Solving 3.5 + x2 = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = -4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = -4.272001873 + -3.5 x2 = -4.272001873 + -3.5 Combine like terms: -4.272001873 + -3.5 = -7.772001873 x2 = -7.772001873 Simplifying x2 = -7.772001873 Reorder the terms: 7.772001873 + x2 = -7.772001873 + 7.772001873 Combine like terms: -7.772001873 + 7.772001873 = 0.000000000 7.772001873 + 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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