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Simplifying x4 + -18x2 + 27 = 0 Reorder the terms: 27 + -18x2 + x4 = 0 Solving 27 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -18x2 + -27 + x4 = 0 + -27 Reorder the terms: 27 + -27 + -18x2 + x4 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -18x2 + x4 = 0 + -27 -18x2 + x4 = 0 + -27 Combine like terms: 0 + -27 = -27 -18x2 + x4 = -27 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 = -27 + 81 Reorder the terms: 81 + -18x2 + x4 = -27 + 81 Combine like terms: -27 + 81 = 54 81 + -18x2 + x4 = 54 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x2 + -9) equal to 7.348469228 and -7.348469228.Subproblem 1
x2 + -9 = 7.348469228 Simplifying x2 + -9 = 7.348469228 Reorder the terms: -9 + x2 = 7.348469228 Solving -9 + x2 = 7.348469228 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 = 7.348469228 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 7.348469228 + 9 x2 = 7.348469228 + 9 Combine like terms: 7.348469228 + 9 = 16.348469228 x2 = 16.348469228 Simplifying x2 = 16.348469228 Take the square root of each side: x = {-4.043324032, 4.043324032}Subproblem 2
x2 + -9 = -7.348469228 Simplifying x2 + -9 = -7.348469228 Reorder the terms: -9 + x2 = -7.348469228 Solving -9 + x2 = -7.348469228 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 = -7.348469228 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -7.348469228 + 9 x2 = -7.348469228 + 9 Combine like terms: -7.348469228 + 9 = 1.651530772 x2 = 1.651530772 Simplifying x2 = 1.651530772 Take the square root of each side: x = {-1.285118972, 1.285118972}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.043324032, 4.043324032, -1.285118972, 1.285118972}
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