Solve 50y=(x-1)^2+2(x-1)+1

$$50 y = ( x - 1 ) ^ { 2 } + 2 ( x - 1 ) + 1$$

Solve for y

$$y=\frac{x^{2}}{50}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$50y=x^{2}-2x+1+2\left(x-1\right)+1$$

Use the distributive property to multiply 2 by x-1.

$$50y=x^{2}-2x+1+2x-2+1$$

Combine -2x and 2x to get 0.

$$50y=x^{2}+1-2+1$$

Subtract 2 from 1 to get -1.

$$50y=x^{2}-1+1$$

Add -1 and 1 to get 0.

$$50y=x^{2}$$

Divide both sides by 50.

$$\frac{50y}{50}=\frac{x^{2}}{50}$$

Dividing by 50 undoes the multiplication by 50.

$$y=\frac{x^{2}}{50}$$

Solve for x (complex solution)

$$x=-5\sqrt{2y}$$

$$x=5\sqrt{2y}$$

Solve for x

$$x=5\sqrt{2y}$$

$$x=-5\sqrt{2y}\text{, }y\geq 0$$