Solve (x+1)^2=4(2)(y-6)

$$( x + 1 ) ^ { 2 } = 4 ( 2 ) ( y - 6 )$$

Solve for y

$$y=\frac{\left(x+1\right)^{2}+48}{8}$$

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}.

$$x^{2}+2x+1=4\times 2\left(y-6\right)$$

Multiply 4 and 2 to get 8.

$$x^{2}+2x+1=8\left(y-6\right)$$

Use the distributive property to multiply 8 by y-6.

$$x^{2}+2x+1=8y-48$$

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

$$8y-48=x^{2}+2x+1$$

Add 48 to both sides.

$$8y=x^{2}+2x+1+48$$

Add 1 and 48 to get 49.

$$8y=x^{2}+2x+49$$

Divide both sides by 8.

$$\frac{8y}{8}=\frac{x^{2}+2x+49}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$y=\frac{x^{2}+2x+49}{8}$$

Divide x^{2}+2x+49 by 8.

$$y=\frac{x^{2}}{8}+\frac{x}{4}+\frac{49}{8}$$

Solve for x (complex solution)

$$x=-2\sqrt{2\left(y-6\right)}-1$$

$$x=2\sqrt{2\left(y-6\right)}-1$$

Solve for x

$$x=-2\sqrt{2\left(y-6\right)}-1$$

$$x=2\sqrt{2\left(y-6\right)}-1\text{, }y\geq 6$$