Solve P(x)+P(x-1)=2x^2-4x+2

$$P ( x ) + P ( x - 1 ) = 2 x ^ { 2 } - 4 x + 2$$

Solve for P

$$P=\frac{2\left(x-1\right)^{2}}{2x-1}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply P by x-1.

$$Px+Px-P=2x^{2}-4x+2$$

Combine Px and Px to get 2Px.

$$2Px-P=2x^{2}-4x+2$$

Combine all terms containing P.

$$\left(2x-1\right)P=2x^{2}-4x+2$$

Divide both sides by 2x-1.

$$\frac{\left(2x-1\right)P}{2x-1}=\frac{2\left(x-1\right)^{2}}{2x-1}$$

Dividing by 2x-1 undoes the multiplication by 2x-1.

$$P=\frac{2\left(x-1\right)^{2}}{2x-1}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{P\left(P+2\right)}+P+2}{2}$$

$$x=\frac{\sqrt{P\left(P+2\right)}+P+2}{2}$$

Solve for x

$$x=\frac{-\sqrt{P\left(P+2\right)}+P+2}{2}$$

$$x=\frac{\sqrt{P\left(P+2\right)}+P+2}{2}\text{, }P\leq -2\text{ or }P\geq 0$$