Question

How do you solve `1/4b^2=16`?

Answer 1

`b^2=64` or `b=8`

Explanation:

Expand both sides by 4:
`(4b^2)/4=4*16`

Now you have
`b^2=64`

Take square root (both sides)
`sqrt(b^2)=sqrt64`

`b=8`

Answer 2

`b=+-8`

Explanation:

`color(blue)"Isolate " b^2" by multiplying both sides by 4"`

`cancel(4)^1xx1/cancel(4)^1b^2=4xx16`

`rArrb^2=64`

`color(blue)"take the square root of both sides"`

`sqrt(b^2)=color(red)(+-)sqrt64`

`rArrb=color(red)(+-)8`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`x=color(red)(+8)to1/4xx8^2=1/4xx64=16`

`x=color(red)(-8)to1/4xx(-8)^2=1/4xx64=16`

`rArrx=+-8" are the solutions"`