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Simplifying x4 + -18x2 + -117 = 0 Reorder the terms: -117 + -18x2 + x4 = 0 Solving -117 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + -18x2 + 117 + x4 = 0 + 117 Reorder the terms: -117 + 117 + -18x2 + x4 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + -18x2 + x4 = 0 + 117 -18x2 + x4 = 0 + 117 Combine like terms: 0 + 117 = 117 -18x2 + x4 = 117 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 = 117 + 81 Reorder the terms: 81 + -18x2 + x4 = 117 + 81 Combine like terms: 117 + 81 = 198 81 + -18x2 + x4 = 198 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 198 Calculate the square root of the right side: 14.071247279 Break this problem into two subproblems by setting (x2 + -9) equal to 14.071247279 and -14.071247279.Subproblem 1
x2 + -9 = 14.071247279 Simplifying x2 + -9 = 14.071247279 Reorder the terms: -9 + x2 = 14.071247279 Solving -9 + x2 = 14.071247279 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 = 14.071247279 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 14.071247279 + 9 x2 = 14.071247279 + 9 Combine like terms: 14.071247279 + 9 = 23.071247279 x2 = 23.071247279 Simplifying x2 = 23.071247279 Take the square root of each side: x = {-4.803253822, 4.803253822}Subproblem 2
x2 + -9 = -14.071247279 Simplifying x2 + -9 = -14.071247279 Reorder the terms: -9 + x2 = -14.071247279 Solving -9 + x2 = -14.071247279 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 = -14.071247279 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -14.071247279 + 9 x2 = -14.071247279 + 9 Combine like terms: -14.071247279 + 9 = -5.071247279 x2 = -5.071247279 Simplifying x2 = -5.071247279 Reorder the terms: 5.071247279 + x2 = -5.071247279 + 5.071247279 Combine like terms: -5.071247279 + 5.071247279 = 0.000000000 5.071247279 + 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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