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Simplifying x4 + -12x2 + 4 = 0 Reorder the terms: 4 + -12x2 + x4 = 0 Solving 4 + -12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -12x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -12x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -12x2 + x4 = 0 + -4 -12x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -12x2 + x4 = -4 The x term is -12x2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x2 + 36 + x4 = -4 + 36 Reorder the terms: 36 + -12x2 + x4 = -4 + 36 Combine like terms: -4 + 36 = 32 36 + -12x2 + x4 = 32 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x2 + -6) equal to 5.656854249 and -5.656854249.Subproblem 1
x2 + -6 = 5.656854249 Simplifying x2 + -6 = 5.656854249 Reorder the terms: -6 + x2 = 5.656854249 Solving -6 + x2 = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 5.656854249 + 6 x2 = 5.656854249 + 6 Combine like terms: 5.656854249 + 6 = 11.656854249 x2 = 11.656854249 Simplifying x2 = 11.656854249 Take the square root of each side: x = {-3.414213562, 3.414213562}Subproblem 2
x2 + -6 = -5.656854249 Simplifying x2 + -6 = -5.656854249 Reorder the terms: -6 + x2 = -5.656854249 Solving -6 + x2 = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -5.656854249 + 6 x2 = -5.656854249 + 6 Combine like terms: -5.656854249 + 6 = 0.343145751 x2 = 0.343145751 Simplifying x2 = 0.343145751 Take the square root of each side: x = {-0.585786438, 0.585786438}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.414213562, 3.414213562, -0.585786438, 0.585786438}
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