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Simplifying x4 + -18x2 + 1 = 0 Reorder the terms: 1 + -18x2 + x4 = 0 Solving 1 + -18x2 + 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 + -18x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -18x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -18x2 + x4 = 0 + -1 -18x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -18x2 + x4 = -1 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 = -1 + 81 Reorder the terms: 81 + -18x2 + x4 = -1 + 81 Combine like terms: -1 + 81 = 80 81 + -18x2 + x4 = 80 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x2 + -9) equal to 8.94427191 and -8.94427191.Subproblem 1
x2 + -9 = 8.94427191 Simplifying x2 + -9 = 8.94427191 Reorder the terms: -9 + x2 = 8.94427191 Solving -9 + x2 = 8.94427191 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 = 8.94427191 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 8.94427191 + 9 x2 = 8.94427191 + 9 Combine like terms: 8.94427191 + 9 = 17.94427191 x2 = 17.94427191 Simplifying x2 = 17.94427191 Take the square root of each side: x = {-4.236067978, 4.236067978}Subproblem 2
x2 + -9 = -8.94427191 Simplifying x2 + -9 = -8.94427191 Reorder the terms: -9 + x2 = -8.94427191 Solving -9 + x2 = -8.94427191 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 = -8.94427191 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -8.94427191 + 9 x2 = -8.94427191 + 9 Combine like terms: -8.94427191 + 9 = 0.05572809 x2 = 0.05572809 Simplifying x2 = 0.05572809 Take the square root of each side: x = {-0.236067977, 0.236067977}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.236067978, 4.236067978, -0.236067977, 0.236067977}
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