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Simplifying x4 + -18x2 + -36 = 0 Reorder the terms: -36 + -18x2 + x4 = 0 Solving -36 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -18x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + -18x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -18x2 + x4 = 0 + 36 -18x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 -18x2 + x4 = 36 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 = 36 + 81 Reorder the terms: 81 + -18x2 + x4 = 36 + 81 Combine like terms: 36 + 81 = 117 81 + -18x2 + x4 = 117 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x2 + -9) equal to 10.816653826 and -10.816653826.Subproblem 1
x2 + -9 = 10.816653826 Simplifying x2 + -9 = 10.816653826 Reorder the terms: -9 + x2 = 10.816653826 Solving -9 + x2 = 10.816653826 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 = 10.816653826 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 10.816653826 + 9 x2 = 10.816653826 + 9 Combine like terms: 10.816653826 + 9 = 19.816653826 x2 = 19.816653826 Simplifying x2 = 19.816653826 Take the square root of each side: x = {-4.451590033, 4.451590033}Subproblem 2
x2 + -9 = -10.816653826 Simplifying x2 + -9 = -10.816653826 Reorder the terms: -9 + x2 = -10.816653826 Solving -9 + x2 = -10.816653826 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 = -10.816653826 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -10.816653826 + 9 x2 = -10.816653826 + 9 Combine like terms: -10.816653826 + 9 = -1.816653826 x2 = -1.816653826 Simplifying x2 = -1.816653826 Reorder the terms: 1.816653826 + x2 = -1.816653826 + 1.816653826 Combine like terms: -1.816653826 + 1.816653826 = 0.000000000 1.816653826 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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