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Simplifying x4 + 6x2 + -3 = 0 Reorder the terms: -3 + 6x2 + x4 = 0 Solving -3 + 6x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 6x2 + 3 + x4 = 0 + 3 Reorder the terms: -3 + 3 + 6x2 + x4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6x2 + x4 = 0 + 3 6x2 + x4 = 0 + 3 Combine like terms: 0 + 3 = 3 6x2 + x4 = 3 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 = 3 + 9 Reorder the terms: 9 + 6x2 + x4 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6x2 + x4 = 12 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x2 + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
x2 + 3 = 3.464101615 Simplifying x2 + 3 = 3.464101615 Reorder the terms: 3 + x2 = 3.464101615 Solving 3 + x2 = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 3.464101615 + -3 x2 = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 x2 = 0.464101615 Simplifying x2 = 0.464101615 Take the square root of each side: x = {-0.681250039, 0.681250039}Subproblem 2
x2 + 3 = -3.464101615 Simplifying x2 + 3 = -3.464101615 Reorder the terms: 3 + x2 = -3.464101615 Solving 3 + x2 = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -3.464101615 + -3 x2 = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 x2 = -6.464101615 Simplifying x2 = -6.464101615 Reorder the terms: 6.464101615 + x2 = -6.464101615 + 6.464101615 Combine like terms: -6.464101615 + 6.464101615 = 0.000000000 6.464101615 + 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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