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Simplifying 0 = x4 + -18x2 + -27 Reorder the terms: 0 = -27 + -18x2 + x4 Solving 0 = -27 + -18x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 27 = 27 27 + 18x2 + -1x4 = -27 + -18x2 + x4 + 27 + 18x2 + -1x4 Reorder the terms: 27 + 18x2 + -1x4 = -27 + 27 + -18x2 + 18x2 + x4 + -1x4 Combine like terms: -27 + 27 = 0 27 + 18x2 + -1x4 = 0 + -18x2 + 18x2 + x4 + -1x4 27 + 18x2 + -1x4 = -18x2 + 18x2 + x4 + -1x4 Combine like terms: -18x2 + 18x2 = 0 27 + 18x2 + -1x4 = 0 + x4 + -1x4 27 + 18x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 27 + 18x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + -18x2 + x4 = 0 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 = 108 81 + -18x2 + x4 = 108 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x2 + -9) equal to 10.392304845 and -10.392304845.Subproblem 1
x2 + -9 = 10.392304845 Simplifying x2 + -9 = 10.392304845 Reorder the terms: -9 + x2 = 10.392304845 Solving -9 + x2 = 10.392304845 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 = 10.392304845 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 10.392304845 + 9 x2 = 10.392304845 + 9 Combine like terms: 10.392304845 + 9 = 19.392304845 x2 = 19.392304845 Simplifying x2 = 19.392304845 Take the square root of each side: x = {-4.403669475, 4.403669475}Subproblem 2
x2 + -9 = -10.392304845 Simplifying x2 + -9 = -10.392304845 Reorder the terms: -9 + x2 = -10.392304845 Solving -9 + x2 = -10.392304845 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 = -10.392304845 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -10.392304845 + 9 x2 = -10.392304845 + 9 Combine like terms: -10.392304845 + 9 = -1.392304845 x2 = -1.392304845 Simplifying x2 = -1.392304845 Reorder the terms: 1.392304845 + x2 = -1.392304845 + 1.392304845 Combine like terms: -1.392304845 + 1.392304845 = 0.000000000 1.392304845 + 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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