Question

How do you solve the equation `5(x-4)^2=125`?

Answer 1

`x=-1" or " x=9`

Explanation:

`color(blue)"Isolate " (x-4)^2" by dividing both sides by 5"`

`(cancel(5)(x-4)^2)/cancel(5)=125/5`

`rArr(x-4)^2=25`

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

`sqrt((x-4)^2)=color(red)(+-)sqrt25larr" note plus or minus"`

`rArrx-4=+-5`

`"add 4 to both sides"`

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

`rArrx=4+-5`

`rArrx=4+5=9" or " x=4-5=-1`

`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=-1to5(-1-4)^2=5xx5^2=125`

`x=9to5(9-4)^2=5xx5^2=125`

`rArrx=-1" or " x=9" are the solutions"`