Solve 1/2(y+4)=(x-7)^2

$$1 / 2 ( y + 4 ) = ( x - 7 ) ^ { 2 }$$

Solve for y

$$y=2\left(\left(x-7\right)^{2}-2\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by y+4.

$$\frac{1}{2}y+2=\left(x-7\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7\right)^{2}.

$$\frac{1}{2}y+2=x^{2}-14x+49$$

Subtract 2 from both sides.

$$\frac{1}{2}y=x^{2}-14x+49-2$$

Subtract 2 from 49 to get 47.

$$\frac{1}{2}y=x^{2}-14x+47$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}y}{\frac{1}{2}}=\frac{x^{2}-14x+47}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$y=\frac{x^{2}-14x+47}{\frac{1}{2}}$$

Divide x^{2}-14x+47 by \frac{1}{2} by multiplying x^{2}-14x+47 by the reciprocal of \frac{1}{2}.

$$y=2x^{2}-28x+94$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2y+8}}{2}+7$$

$$x=\frac{\sqrt{2y+8}}{2}+7$$

Solve for x

$$x=-\frac{\sqrt{2y+8}}{2}+7$$

$$x=\frac{\sqrt{2y+8}}{2}+7\text{, }y\geq -4$$