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Simplifying P(x) = -2x2 + 2x Multiply P * x xP = -2x2 + 2x Reorder the terms: xP = 2x + -2x2 Solving xP = 2x + -2x2 Solving for variable 'x'. Reorder the terms: -2x + xP + 2x2 = 2x + -2x2 + -2x + 2x2 Reorder the terms: -2x + xP + 2x2 = 2x + -2x + -2x2 + 2x2 Combine like terms: 2x + -2x = 0 -2x + xP + 2x2 = 0 + -2x2 + 2x2 -2x + xP + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -2x + xP + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + P + 2x) = 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 + P + 2x)' equal to zero and attempt to solve: Simplifying -2 + P + 2x = 0 Solving -2 + P + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + P + 2 + 2x = 0 + 2 Reorder the terms: -2 + 2 + P + 2x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + P + 2x = 0 + 2 P + 2x = 0 + 2 Combine like terms: 0 + 2 = 2 P + 2x = 2 Add '-1P' to each side of the equation. P + -1P + 2x = 2 + -1P Combine like terms: P + -1P = 0 0 + 2x = 2 + -1P 2x = 2 + -1P Divide each side by '2'. x = 1 + -0.5P Simplifying x = 1 + -0.5PSolution
x = {0, 1 + -0.5P}
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