need help solving this equation by using the square root (1-x)^2 = 4
i need help solving (1-x)^2 = 4
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
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 true.to 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)2 = 4 (1 - (-1))2=4
(-2)2 = 4 (1 + 1)2 =4
4 = 4 (2)2 = 4
So both answers are correct thus your solutions are x=-1 and x=3