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Simplifying x2 + 3x + 1 = x + 1 Reorder the terms: 1 + 3x + x2 = x + 1 Reorder the terms: 1 + 3x + x2 = 1 + x Add '-1' to each side of the equation. 1 + 3x + -1 + x2 = 1 + -1 + x Reorder the terms: 1 + -1 + 3x + x2 = 1 + -1 + x Combine like terms: 1 + -1 = 0 0 + 3x + x2 = 1 + -1 + x 3x + x2 = 1 + -1 + x Combine like terms: 1 + -1 = 0 3x + x2 = 0 + x 3x + x2 = x Solving 3x + x2 = x Solving for variable 'x'. Reorder the terms: 3x + -1x + x2 = x + -1x Combine like terms: 3x + -1x = 2x 2x + x2 = x + -1x Combine like terms: x + -1x = 0 2x + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(2 + x) = 0Subproblem 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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