Question 498825
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Solve and check the quadratic equation below by taking the square root of both sides. Express irrational answers in rational form.
(x-10)^2=4
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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.



<pre>
Your starting equation is

    (x-10)^2 = 4.    (1)


Take square root of both sides.  You will get

    x-10 = +/-2.         <<<---===  square root of 4 has two values: 2 and -2.


It means that we have two cases.


Case 1.  x-10 = 2.   Then  x = 2+10 = 12.

Case 2.  x-10 = -2.  Then  x = -2+10 = 8.


So, equation (1) has two solutions.  They are  x = 8  and  x = 12.


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

Solved correctly.


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It might seem the loss of roots is a minor issue.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In fact, &nbsp;it is not so.


Loss of roots is a failed test of understanding square roots. 
So, solving this equation correctly or incorrectly is an easy way 
to check if a person does understand the subject.
In 10 seconds, everything becomes clear.



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Notice that the problem's formulation is like a lame horse with three legs.



Indeed, &nbsp;it says &nbsp;" Express irrational answers in rational form. "


Firstly, &nbsp;it is &nbsp;IMPOSSIBLE &nbsp;to do.


Secondly, &nbsp;it shows that a person, &nbsp;who wrote it, &nbsp;is mathematically illiterate.