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

$$( 2 x - 1 ) x + 2 x + y = 1$$

Solve for y

$$y=-x\left(2x+1\right)+1$$

Solution Steps

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

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

Combine -x and 2x to get x.

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

Subtract 2x^{2} from both sides.

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

Subtract x from both sides.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{9-8y}-1}{4}$$

$$x=\frac{-\sqrt{9-8y}-1}{4}$$

Solve for x

$$x=\frac{\sqrt{9-8y}-1}{4}$$

$$x=\frac{-\sqrt{9-8y}-1}{4}\text{, }y\leq \frac{9}{8}$$