Solve Square Root Method: (x-1)^2 = 4

[elflacodepr]

Homework Statement

(x - 1)^2 = 4

The Attempt at a Solution

This is what I've done

(x - 1)^2 = 4

Everything inside parenthesis goes to: ^2
x^2 - 1^2 = 4

now we got
x^2 - 1 = 4

Now (I think) I use the square root method
x^2 - 1 = √4
x^2 - 1 = 2

Now I factorize:
(x - 1) (x +1) = 2

This is what I've done for now, shall I make √ on both sides in this equation x^2 - 1 = √4?

 

[rock.freak667]

(x-1)²≠x²-1

(a+b)²=a²+b²+2ab

you can also take the square root initially and check the two cases

X²=A => X=±√A i.e. X= +√A or X=-√A

 

[elflacodepr]

Thanks, All I did now is use the square root right on start:

√(x - 1)^2 = √4

So now we go this:

x - 1 = ±2

which gives me the following results:

x - 1 = ±2
x = 2 + 1
x = 3

OR

x - 1 = ±2
x = -2 + 1
x = -1

 

[rock.freak667]

Thanks, All I did now is use the square root right on start:

√(x - 1)^2 = √4

So now we go this:

x - 1 = ±2

which gives me the following results:

x - 1 = ±2
x = 2 + 1
x = 3

OR

x - 1 = ±2
x = -2 + 1
x = -1

Good. This is correct because if we put x=3 or x=-1 into (x-1)², we ill get '4'.

 

[elflacodepr]

Thanks!