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Simplifying x4 + 18x2 + 69 = 0 Reorder the terms: 69 + 18x2 + x4 = 0 Solving 69 + 18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-69' to each side of the equation. 69 + 18x2 + -69 + x4 = 0 + -69 Reorder the terms: 69 + -69 + 18x2 + x4 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + 18x2 + x4 = 0 + -69 18x2 + x4 = 0 + -69 Combine like terms: 0 + -69 = -69 18x2 + x4 = -69 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 = -69 + 81 Reorder the terms: 81 + 18x2 + x4 = -69 + 81 Combine like terms: -69 + 81 = 12 81 + 18x2 + x4 = 12 Factor a perfect square on the left side: (x2 + 9)(x2 + 9) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x2 + 9) equal to 3.464101615 and -3.464101615.Subproblem 1
x2 + 9 = 3.464101615 Simplifying x2 + 9 = 3.464101615 Reorder the terms: 9 + x2 = 3.464101615 Solving 9 + x2 = 3.464101615 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 = 3.464101615 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = 3.464101615 + -9 x2 = 3.464101615 + -9 Combine like terms: 3.464101615 + -9 = -5.535898385 x2 = -5.535898385 Simplifying x2 = -5.535898385 Reorder the terms: 5.535898385 + x2 = -5.535898385 + 5.535898385 Combine like terms: -5.535898385 + 5.535898385 = 0.000000000 5.535898385 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 9 = -3.464101615 Simplifying x2 + 9 = -3.464101615 Reorder the terms: 9 + x2 = -3.464101615 Solving 9 + x2 = -3.464101615 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 = -3.464101615 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = -3.464101615 + -9 x2 = -3.464101615 + -9 Combine like terms: -3.464101615 + -9 = -12.464101615 x2 = -12.464101615 Simplifying x2 = -12.464101615 Reorder the terms: 12.464101615 + x2 = -12.464101615 + 12.464101615 Combine like terms: -12.464101615 + 12.464101615 = 0.000000000 12.464101615 + 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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