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Simplifying P(x) = -2x2 + 6x Multiply P * x xP = -2x2 + 6x Reorder the terms: xP = 6x + -2x2 Solving xP = 6x + -2x2 Solving for variable 'x'. Reorder the terms: -6x + xP + 2x2 = 6x + -2x2 + -6x + 2x2 Reorder the terms: -6x + xP + 2x2 = 6x + -6x + -2x2 + 2x2 Combine like terms: 6x + -6x = 0 -6x + xP + 2x2 = 0 + -2x2 + 2x2 -6x + xP + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -6x + xP + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 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 '(-6 + P + 2x)' equal to zero and attempt to solve: Simplifying -6 + P + 2x = 0 Solving -6 + P + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + P + 6 + 2x = 0 + 6 Reorder the terms: -6 + 6 + P + 2x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + P + 2x = 0 + 6 P + 2x = 0 + 6 Combine like terms: 0 + 6 = 6 P + 2x = 6 Add '-1P' to each side of the equation. P + -1P + 2x = 6 + -1P Combine like terms: P + -1P = 0 0 + 2x = 6 + -1P 2x = 6 + -1P Divide each side by '2'. x = 3 + -0.5P Simplifying x = 3 + -0.5PSolution
x = {0, 3 + -0.5P}
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