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Simplifying x4 + -22x2 + 1 = 0 Reorder the terms: 1 + -22x2 + x4 = 0 Solving 1 + -22x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -22x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -22x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -22x2 + x4 = 0 + -1 -22x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -22x2 + x4 = -1 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 = -1 + 121 Reorder the terms: 121 + -22x2 + x4 = -1 + 121 Combine like terms: -1 + 121 = 120 121 + -22x2 + x4 = 120 Factor a perfect square on the left side: (x2 + -11)(x2 + -11) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x2 + -11) equal to 10.95445115 and -10.95445115.Subproblem 1
x2 + -11 = 10.95445115 Simplifying x2 + -11 = 10.95445115 Reorder the terms: -11 + x2 = 10.95445115 Solving -11 + x2 = 10.95445115 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 = 10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = 10.95445115 + 11 x2 = 10.95445115 + 11 Combine like terms: 10.95445115 + 11 = 21.95445115 x2 = 21.95445115 Simplifying x2 = 21.95445115 Take the square root of each side: x = {-4.68555772, 4.68555772}Subproblem 2
x2 + -11 = -10.95445115 Simplifying x2 + -11 = -10.95445115 Reorder the terms: -11 + x2 = -10.95445115 Solving -11 + x2 = -10.95445115 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 = -10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = -10.95445115 + 11 x2 = -10.95445115 + 11 Combine like terms: -10.95445115 + 11 = 0.04554885 x2 = 0.04554885 Simplifying x2 = 0.04554885 Take the square root of each side: x = {-0.213421766, 0.213421766}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.68555772, 4.68555772, -0.213421766, 0.213421766}
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