Question

How do you solve `7(x-4)^2-2=54` using any method?

Answer 1

`x=4+-2sqrt2`

Explanation:

`color(blue)"Isolate " (x-4)^2" on the left side"`

`"add 2 to each side"`

`7(x-4)^2cancel(-2)cancel(+2)=54+2`

`rArr7(x-4)^2=56`

`"divide both sides by 7"`

`(cancel(7)(x-4)^2)/cancel(7)=56/7`

`rArr(x-4)^2=8`

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

`sqrt((x-4)^2)=+-sqrt8rarr(sqrt8=sqrt(4xx2))`

`rArrx-4=+-2sqrt2`

`rArrx=4+-2sqrt2`

Answer 2

`x=4+-2sqrt2`

Explanation:

`7(x-4)^2=56`
`(x-4)^2=8`
`x-4=+-2sqrt2`
`x=4+-2sqrt2`