Question 1135104
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<pre>
{{{x^2 + 6x + 12}}} = {{{(x^2 + 6x + 9)}}} + 3 = {{{(x+3)^2}}} + 3.


So, this expression is the sum of two terms.


First term is quadratic binomial  {{{(x+3)^2}}},  which ALWAYS is non-negative as a square of a real number.


The second term is constant term "3", which is positive, too.


Therefore, their sum is ALWAYS positive.


Thus, the original expression is always positive, too.
</pre>

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It is a TEMPLATE and a SAMPLE to you on how this and similar problems should be solved and worded.


The method which I used &nbsp;is called  "completing the square".


On how this method works, &nbsp;you can read from the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Learning-by-examples-on-HOW-TO-complete-the-square.lesson>HOW TO complete the square - Learning by examples</A> 

in this site.



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