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Simplifying 1 = (1 + x)(1 + x) Multiply (1 + x) * (1 + x) 1 = (1(1 + x) + x(1 + x)) 1 = ((1 * 1 + x * 1) + x(1 + x)) 1 = ((1 + 1x) + x(1 + x)) 1 = (1 + 1x + (1 * x + x * x)) 1 = (1 + 1x + (1x + x2)) Combine like terms: 1x + 1x = 2x 1 = (1 + 2x + x2) Add '-1' to each side of the equation. 1 + -1 = 1 + 2x + -1 + x2 Combine like terms: 1 + -1 = 0 0 = 1 + 2x + -1 + x2 Reorder the terms: 0 = 1 + -1 + 2x + x2 Combine like terms: 1 + -1 = 0 0 = 0 + 2x + x2 0 = 2x + x2 Solving 0 = 2x + x2 Solving for variable 'x'. Remove the zero: -2x + -1x2 = 2x + x2 + -2x + -1x2 Reorder the terms: -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -2x + -1x2 = 0 + x2 + -1x2 -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(2 + x) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {0, -2}
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