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Simplifying x4 + 7x2 + -16 = 0 Reorder the terms: -16 + 7x2 + x4 = 0 Solving -16 + 7x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 7x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + 7x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7x2 + x4 = 0 + 16 7x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 7x2 + x4 = 16 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 = 16 + 12.25 Reorder the terms: 12.25 + 7x2 + x4 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + 7x2 + x4 = 28.25 Factor a perfect square on the left side: (x2 + 3.5)(x2 + 3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x2 + 3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x2 + 3.5 = 5.315072906 Simplifying x2 + 3.5 = 5.315072906 Reorder the terms: 3.5 + x2 = 5.315072906 Solving 3.5 + x2 = 5.315072906 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 = 5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = 5.315072906 + -3.5 x2 = 5.315072906 + -3.5 Combine like terms: 5.315072906 + -3.5 = 1.815072906 x2 = 1.815072906 Simplifying x2 = 1.815072906 Take the square root of each side: x = {-1.347246416, 1.347246416}Subproblem 2
x2 + 3.5 = -5.315072906 Simplifying x2 + 3.5 = -5.315072906 Reorder the terms: 3.5 + x2 = -5.315072906 Solving 3.5 + x2 = -5.315072906 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 = -5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = -5.315072906 + -3.5 x2 = -5.315072906 + -3.5 Combine like terms: -5.315072906 + -3.5 = -8.815072906 x2 = -8.815072906 Simplifying x2 = -8.815072906 Reorder the terms: 8.815072906 + x2 = -8.815072906 + 8.815072906 Combine like terms: -8.815072906 + 8.815072906 = 0.000000000 8.815072906 + 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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