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