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Simplifying x4 + -22x2 + 9 = 0 Reorder the terms: 9 + -22x2 + x4 = 0 Solving 9 + -22x2 + 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 + -22x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -22x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -22x2 + x4 = 0 + -9 -22x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -22x2 + x4 = -9 The x term is -22x2. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x2 + 121 + x4 = -9 + 121 Reorder the terms: 121 + -22x2 + x4 = -9 + 121 Combine like terms: -9 + 121 = 112 121 + -22x2 + x4 = 112 Factor a perfect square on the left side: (x2 + -11)(x2 + -11) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x2 + -11) equal to 10.583005244 and -10.583005244.Subproblem 1
x2 + -11 = 10.583005244 Simplifying x2 + -11 = 10.583005244 Reorder the terms: -11 + x2 = 10.583005244 Solving -11 + x2 = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x2 = 10.583005244 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = 10.583005244 + 11 x2 = 10.583005244 + 11 Combine like terms: 10.583005244 + 11 = 21.583005244 x2 = 21.583005244 Simplifying x2 = 21.583005244 Take the square root of each side: x = {-4.645751311, 4.645751311}Subproblem 2
x2 + -11 = -10.583005244 Simplifying x2 + -11 = -10.583005244 Reorder the terms: -11 + x2 = -10.583005244 Solving -11 + x2 = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x2 = -10.583005244 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = -10.583005244 + 11 x2 = -10.583005244 + 11 Combine like terms: -10.583005244 + 11 = 0.416994756 x2 = 0.416994756 Simplifying x2 = 0.416994756 Take the square root of each side: x = {-0.645751311, 0.645751311}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.645751311, 4.645751311, -0.645751311, 0.645751311}
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