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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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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)

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


Gene G. | You can do it! I'll show you how.You can do it! I'll show you how.
5.0 5.0 (254 lesson ratings) (254)

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

Blerta L. | "The very professional and friendly tutor of Oak Forest"."The very professional and friendly tuto...

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. 

Courtney C. | Collegiate Tutor Specializing in MathCollegiate Tutor Specializing in Math
4.7 4.7 (6 lesson ratings) (6)

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