Solve x=(y+2)(y+1)+3y+2

$$x = ( y + 2 ) ( y + 1 ) + 3 y + 2$$

Solve for x

$$x=y^{2}+6y+4$$

Solution Steps

Use the distributive property to multiply y+2 by y+1 and combine like terms.

$$x=y^{2}+3y+2+3y+2$$

Combine 3y and 3y to get 6y.

$$x=y^{2}+6y+2+2$$

Add 2 and 2 to get 4.

$$x=y^{2}+6y+4$$

Solve for y (complex solution)

$$y=\sqrt{x+5}-3$$

$$y=-\sqrt{x+5}-3$$

Solve for y

$$y=\sqrt{x+5}-3$$

$$y=-\sqrt{x+5}-3\text{, }x\geq -5$$