Question

How do you solve `3(x - 1)^2= 27`?

Answer 1

`x = 10`

Explanation:

`3(x-1)^2 = 27`

First, divide both sides by `color(blue)3`:
`(3(x-1)^2)/color(blue)3 = 27/color(blue)3`

`(x-1)^2 = 9`

Now square root both sides:
`sqrt((x-1)^2) = sqrt9`

`x - 1 = \pm3`

Finally, add `color(blue)1` to both sides:
`x - 1 quadcolor(blue)(+quad1) = \pm3 quadcolor(blue)(+quad1)`

Therefore,
`x = 4 or -2`

Hope this helps!

Answer 2

`x=-2" or "x=4`

Explanation:

`"divide both sides by 3"`

`cancel(3)/cancel(3)(x-1)^2=9`

`(x-1)^2=9`

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

`sqrt((x-1)^2)=+-sqrt9larrcolor(blue)"note plus or minus"`

`x-1=+-3`

`"add 1 to both sides"`

`x=1+-3`

`x=1-3=-2" or "x=1+3=4`