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Simplifying x4 + 6x2 + -9 = 0 Reorder the terms: -9 + 6x2 + x4 = 0 Solving -9 + 6x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 6x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + 6x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6x2 + x4 = 0 + 9 6x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 6x2 + x4 = 9 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 = 9 + 9 Reorder the terms: 9 + 6x2 + x4 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6x2 + x4 = 18 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x2 + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
x2 + 3 = 4.242640687 Simplifying x2 + 3 = 4.242640687 Reorder the terms: 3 + x2 = 4.242640687 Solving 3 + x2 = 4.242640687 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 = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 4.242640687 + -3 x2 = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 x2 = 1.242640687 Simplifying x2 = 1.242640687 Take the square root of each side: x = {-1.114737945, 1.114737945}Subproblem 2
x2 + 3 = -4.242640687 Simplifying x2 + 3 = -4.242640687 Reorder the terms: 3 + x2 = -4.242640687 Solving 3 + x2 = -4.242640687 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 = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -4.242640687 + -3 x2 = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 x2 = -7.242640687 Simplifying x2 = -7.242640687 Reorder the terms: 7.242640687 + x2 = -7.242640687 + 7.242640687 Combine like terms: -7.242640687 + 7.242640687 = 0.000000000 7.242640687 + 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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