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i need help solving (1-x)^2 = 4

need help solving this equation by using the square root (1-x)^2 = 4

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4 Answers

Hello Reggie,

I am from Phoenix too.

The problem (1-x)^2 = 4 can be solved quickly.

First, you should know (1-x)^2 = (x-1)^2 

(x-1)^2 = 4 means what number squared is 4. You know (±2)^2 = 4.

So, x-1 = ±2

x = 3 and x = -1 <==Answer


This is just a slightly different twist on Robert's answer, which is quite good!

You can take the square root of both sides of the equation:

(x-1)^2 = 4
√ [(x-1)^2] = √ 4

±(x-1) = ±2         (remember that √a = ±a)

Putting the ± on both sides is redundant, so you can write:
x-1 = ±2

Now solve:
x-1 = 2  and   x-1 = -2

to get the answers:
x = 3   and   x = -1

Reggie, to solve an equation means to find the value(s) of the variable that make that equation solve the equation we need to leave only the x by one side of the "=" and move every other factor by the other side. and to be able to do that, the greatest rule you should follow is: take every factor that is placed on the same same side of the equation as the x, together with the proper +,-,*, or /, and transfer it by the other side of =. By this I mean:

1. if u need to remove a root, you can transfer it by the other side of the = by making of the factor of the root a power ( vice versa, the power gets  transferred by the other side as a root, with it as a factor)

2. If you need to remove a multiplying factor, you transfer it as a divisor on the other side of =, and vice versa

3. To remove an adding factor, you can simply subtract it to the other side of =, and vice versa

and adopting these rules to your specific question, we have: 


according to 1, the power transforms in sqrt.     (1-x)= sqrt4= -2,   Or +2.  (We consider both positive and negative roots)

we now have 1-x=2   And 1-x=-2

to eliminate one step to the solution, in both equations, we remember of what we told on 3. And transfer the -x fron the left side, to the right side, making of it +x, and move the numbers 2 and -2 to the left, changing their signs also in -2, and +2.v like this we have

            1-2=x         And.         1-(-2)= 1+ (+2)= x.

so 1-2= -1=x.       And.            3=x.

The two values we found above of x (x= -1, and x=3) that make the equation true, are the solution to that equation. 

The initial problem is 

(1-x)2 = 4

To solve by using square root you'd would take the square root of both sides. Remember whatever you do to one side you must do to the other. So you'd get

√((1-x)2) = √(4)

Take the square root of both sides. You know the square root of 4 is 2. The square root of any number, polynomial, or variable squared is number, polynomial, variable itself. (i.e. √((3)2) = 3). Therefore you get,

1-x = 2 and 1 - x = -2 

Keep in mind that the square root of any value has both a positive and negative value.

We'll deal with the positive 2 first.

You subtract 1 from both sides to get the variable by itself.

1(-1) - x = 2 - 1

After you simplify you get:

-x = 1 

 But to get x positive you'd divide by -1. 

One root is x = -1


Yet we haven't dealt with 1 - x = -2

Similar to the dealing with the equation with the positive 2 you would subtract 1 from both sides to get x by itself.


1 ( - 1) - x = -2 (- 1)

1 - 1 - x = -2 - 1

-x = -3

Remember that you want positive x and not negative x so we'd have to divide by -1 to get positive x. Keep in mind what you do to one side of the equation must be done to other.

-x/-1 = -3/-1

The other root has x = 3.


Plug back into the equation to make sure it's actually true.

(1 - 3)= 4                     (1 - (-1))2=4

(-2)2 = 4                         (1 + 1)=4

4 = 4                              (2)= 4



So both answers are correct thus your solutions are x=-1 and x=3