Question 558894
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        In his post, tutor @Theo lost some solutions to given equations.

        So,  his treatment of the problem is incomplete.

        I came to bring a correct complete solutions.



- - - - - - - - Equation (1) - - - - - - - - 


<pre>
(x+1)^2 = 9


Take square root of both sides.  You will get

(x+1) = +/-3.


It means that we have two cases.


Case 1.  x+1 = 3.  Then  x = 3-1 = 2.

Case 2.  x+1 = -3.  Then x = -3-1 = -4.


So, equation (1) has two solutions.  They are  x = 2  and  x = -4.


<U>Check</U>.  Substitute these values into equation (1) to make sure that they suit perfectly.
</pre>



- - - - - - - - Equation (2) - - - - - - - - 


<pre>
x^2 = 121


Take square root of both sides.  You will get

x = +/-11.


It means that the equation has two solutions,  x = 11 and x = -11.


<U>CHECK</U>. Substitute these values into equation (2) to make sure that they suit perfectly.
</pre>

Solved correctly.


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It might seem like the loss of negative roots is a minor issue.
In fact, it is not.
Loss of roots is a test of understanding. And this test shows 
whether the person solving this problem understands the meaning of square roots.