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Simplifying x4 + -18x2 + 49 = 0 Reorder the terms: 49 + -18x2 + x4 = 0 Solving 49 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -18x2 + -49 + x4 = 0 + -49 Reorder the terms: 49 + -49 + -18x2 + x4 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -18x2 + x4 = 0 + -49 -18x2 + x4 = 0 + -49 Combine like terms: 0 + -49 = -49 -18x2 + x4 = -49 The x term is -18x2. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x2 + 81 + x4 = -49 + 81 Reorder the terms: 81 + -18x2 + x4 = -49 + 81 Combine like terms: -49 + 81 = 32 81 + -18x2 + x4 = 32 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x2 + -9) equal to 5.656854249 and -5.656854249.Subproblem 1
x2 + -9 = 5.656854249 Simplifying x2 + -9 = 5.656854249 Reorder the terms: -9 + x2 = 5.656854249 Solving -9 + x2 = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = 5.656854249 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 5.656854249 + 9 x2 = 5.656854249 + 9 Combine like terms: 5.656854249 + 9 = 14.656854249 x2 = 14.656854249 Simplifying x2 = 14.656854249 Take the square root of each side: x = {-3.828427125, 3.828427125}Subproblem 2
x2 + -9 = -5.656854249 Simplifying x2 + -9 = -5.656854249 Reorder the terms: -9 + x2 = -5.656854249 Solving -9 + x2 = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = -5.656854249 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -5.656854249 + 9 x2 = -5.656854249 + 9 Combine like terms: -5.656854249 + 9 = 3.343145751 x2 = 3.343145751 Simplifying x2 = 3.343145751 Take the square root of each side: x = {-1.828427125, 1.828427125}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.828427125, 3.828427125, -1.828427125, 1.828427125}
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