Question

How do you solve the equation `(4x-5)^2=64`?

Answer 1

`x = 13/4`

Explanation:

Square root both sides of the equation and simplify:
`sqrt((4x-5)^2) = sqrt(64)`

`4x - 5 = 8`

`4x = 13`

`x = 13/4`

Answer 2

`x=-3/4" or "x=13/4`

Explanation:

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

`sqrt((4x-5)^2)=color(red)(+-)sqrt64`

`rArr4x-5=color(red)(+-)8`

`•"solve "4x-5=color(red)(+)8`

add 5 to both sides.

`4xcancel(-5)cancel(+5)=8+5`

`rArr4x=13`

divide both sides by 4

`(cancel(4) x)/cancel(4)=13/4`

`rArrx=13/4`

`• "solve "4x-5=color(red)(-8)`

`rArr4x-5+5=-8+5`

`rArr4x=-3`

`rArrx=-3/4`

`color(blue)"As a check"`

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

`(cancel(4)^1xx13/cancel(4)^1-5)^2=8^2=64`

`(cancel(4)^1xx-3/cancel(4)^1-5)^2=(-8)^2=64`

`rArrx=-3/4" or "x=13/4" are the solutions"`