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Simplifying x(x + 1) + 1 = 2x + 1 Reorder the terms: x(1 + x) + 1 = 2x + 1 (1 * x + x * x) + 1 = 2x + 1 (1x + x2) + 1 = 2x + 1 Reorder the terms: 1 + 1x + x2 = 2x + 1 Reorder the terms: 1 + 1x + x2 = 1 + 2x Add '-1' to each side of the equation. 1 + 1x + -1 + x2 = 1 + -1 + 2x Reorder the terms: 1 + -1 + 1x + x2 = 1 + -1 + 2x Combine like terms: 1 + -1 = 0 0 + 1x + x2 = 1 + -1 + 2x 1x + x2 = 1 + -1 + 2x Combine like terms: 1 + -1 = 0 1x + x2 = 0 + 2x 1x + x2 = 2x Solving 1x + x2 = 2x Solving for variable 'x'. Reorder the terms: 1x + -2x + x2 = 2x + -2x Combine like terms: 1x + -2x = -1x -1x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -1x + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {0, 1}
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