Solve y=6^2+left(4zright)^2

$$y= { 6 }^{ 2 } + { \left(4z \right) }^{ 2 }$$

Solve for y

$$y=16z^{2}+36$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$y=36+\left(4z\right)^{2}$$

Expand \left(4z\right)^{2}.

$$y=36+4^{2}z^{2}$$

Calculate 4 to the power of 2 and get 16.

$$y=36+16z^{2}$$

Solve for z (complex solution)

$$z=-\frac{\sqrt{y-36}}{4}$$

$$z=\frac{\sqrt{y-36}}{4}$$

Solve for z

$$z=\frac{\sqrt{y-36}}{4}$$

$$z=-\frac{\sqrt{y-36}}{4}\text{, }y\geq 36$$