Solving Quadratic Equations: (t-2)^2=36

[1/2"]

Hey there!
I just want to know that this problem
(t-2)^2=36
can be solved by squaring t-2 so we have the answer as t=8 ,-4
but suppose if I rather do like this that I square root 36 and remove the power on t-2
then

or t- 2= 6
or t=8
here also i get the 8 result but i don't get the -4 one.
But I think it isn't a wrong way to deal ,is it?
I would be very much happy for any help!

 

[rzaidan]

Hi 1/2"
When you take the square root for both sides ,you are to take the absolute values when removing squares; that is t-2=6 or t-2=-6 so you will have
t=8 , t=-4 as you get.
Best regards
Riad Zaidan

 

[Mark44]

Here's another way to look at this without absolute values.
(t - 2)² = 36
<==> (t - 2)² - 36 = 0
<==> ((t - 2) - 6)((t - 2) + 6) = 0
<==> (t - 8)(t + 4) = 0
<==> t = 8 or t = -4

 

[1/2"]

Thanks a lot for helping !

 

[rzaidan]

Hi Mark44 ,
The problem was in ((removing squares)) from both sides by taking square roots and not in finding another way to solve the problem. In general, thanks a lot for you...
Best Regards
Riad Zaidan
Al-Quds Open University