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Simplifying (x2 + x + 1)(x2 + -1x + 1) + -1 = 0 Reorder the terms: (1 + x + x2)(x2 + -1x + 1) + -1 = 0 Reorder the terms: (1 + x + x2)(1 + -1x + x2) + -1 = 0 Multiply (1 + x + x2) * (1 + -1x + x2) (1(1 + -1x + x2) + x(1 + -1x + x2) + x2(1 + -1x + x2)) + -1 = 0 ((1 * 1 + -1x * 1 + x2 * 1) + x(1 + -1x + x2) + x2(1 + -1x + x2)) + -1 = 0 ((1 + -1x + 1x2) + x(1 + -1x + x2) + x2(1 + -1x + x2)) + -1 = 0 (1 + -1x + 1x2 + (1 * x + -1x * x + x2 * x) + x2(1 + -1x + x2)) + -1 = 0 (1 + -1x + 1x2 + (1x + -1x2 + x3) + x2(1 + -1x + x2)) + -1 = 0 (1 + -1x + 1x2 + 1x + -1x2 + x3 + (1 * x2 + -1x * x2 + x2 * x2)) + -1 = 0 (1 + -1x + 1x2 + 1x + -1x2 + x3 + (1x2 + -1x3 + x4)) + -1 = 0 Reorder the terms: (1 + -1x + 1x + 1x2 + -1x2 + 1x2 + x3 + -1x3 + x4) + -1 = 0 Combine like terms: -1x + 1x = 0 (1 + 0 + 1x2 + -1x2 + 1x2 + x3 + -1x3 + x4) + -1 = 0 (1 + 1x2 + -1x2 + 1x2 + x3 + -1x3 + x4) + -1 = 0 Combine like terms: 1x2 + -1x2 = 0 (1 + 0 + 1x2 + x3 + -1x3 + x4) + -1 = 0 (1 + 1x2 + x3 + -1x3 + x4) + -1 = 0 Combine like terms: x3 + -1x3 = 0 (1 + 1x2 + 0 + x4) + -1 = 0 (1 + 1x2 + x4) + -1 = 0 Reorder the terms: 1 + -1 + 1x2 + x4 = 0 Combine like terms: 1 + -1 = 0 0 + 1x2 + x4 = 0 1x2 + x4 = 0 Solving 1x2 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(1 + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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