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Simplifying x4 + -16x2 + 32 = 0 Reorder the terms: 32 + -16x2 + x4 = 0 Solving 32 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -16x2 + -32 + x4 = 0 + -32 Reorder the terms: 32 + -32 + -16x2 + x4 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -16x2 + x4 = 0 + -32 -16x2 + x4 = 0 + -32 Combine like terms: 0 + -32 = -32 -16x2 + x4 = -32 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = -32 + 64 Reorder the terms: 64 + -16x2 + x4 = -32 + 64 Combine like terms: -32 + 64 = 32 64 + -16x2 + x4 = 32 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x2 + -8) equal to 5.656854249 and -5.656854249.Subproblem 1
x2 + -8 = 5.656854249 Simplifying x2 + -8 = 5.656854249 Reorder the terms: -8 + x2 = 5.656854249 Solving -8 + x2 = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 5.656854249 + 8 x2 = 5.656854249 + 8 Combine like terms: 5.656854249 + 8 = 13.656854249 x2 = 13.656854249 Simplifying x2 = 13.656854249 Take the square root of each side: x = {-3.69551813, 3.69551813}Subproblem 2
x2 + -8 = -5.656854249 Simplifying x2 + -8 = -5.656854249 Reorder the terms: -8 + x2 = -5.656854249 Solving -8 + x2 = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -5.656854249 + 8 x2 = -5.656854249 + 8 Combine like terms: -5.656854249 + 8 = 2.343145751 x2 = 2.343145751 Simplifying x2 = 2.343145751 Take the square root of each side: x = {-1.53073373, 1.53073373}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.69551813, 3.69551813, -1.53073373, 1.53073373}
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