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

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

Solve for x

$$x=\frac{\left(y+2\right)^{2}+4}{4}$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 4 by x-1.

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

Swap sides so that all variable terms are on the left hand side.

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

Add 4 to both sides.

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

Add 4 and 4 to get 8.

$$4x=y^{2}+4y+8$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{y^{2}+4y+8}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{y^{2}+4y+8}{4}$$

Divide y^{2}+4y+8 by 4.

$$x=\frac{y^{2}}{4}+y+2$$

Solve for y (complex solution)

$$y=-2\sqrt{x-1}-2$$

$$y=2\sqrt{x-1}-2$$

Solve for y

$$y=-2\sqrt{x-1}-2$$

$$y=2\sqrt{x-1}-2\text{, }x\geq 1$$