Solve (y+4)^2=16(x-1)

$$( y + 4 ) ^ { 2 } = 16 ( x - 1 )$$

Solve for x

$$x=\frac{\left(y+4\right)^{2}+16}{16}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+4\right)^{2}.

$$y^{2}+8y+16=16\left(x-1\right)$$

Use the distributive property to multiply 16 by x-1.

$$y^{2}+8y+16=16x-16$$

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

$$16x-16=y^{2}+8y+16$$

Add 16 to both sides.

$$16x=y^{2}+8y+16+16$$

Add 16 and 16 to get 32.

$$16x=y^{2}+8y+32$$

Divide both sides by 16.

$$\frac{16x}{16}=\frac{y^{2}+8y+32}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$x=\frac{y^{2}+8y+32}{16}$$

Divide y^{2}+8y+32 by 16.

$$x=\frac{y^{2}}{16}+\frac{y}{2}+2$$

Solve for y (complex solution)

$$y=-4\sqrt{x-1}-4$$

$$y=4\sqrt{x-1}-4$$

Solve for y

$$y=-4\sqrt{x-1}-4$$

$$y=4\sqrt{x-1}-4\text{, }x\geq 1$$