Question 1173138
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<pre>

You start with

    x^2 + 6x + 7 = 0


The term 6x says you that the expected square term should be {x+3)^2 = x^2 + 6x + 9


So we add 2 to both sides

    x^2 + 6x + 7 + 2 = 2,   or

    x^2 + 6x + 9 = 2.


In the left side you just have the desired square:

    {x + 3)^2 = 2.


Now take the square root from both sides

    x + 3 = +/- {{{sqrt(2)}}}


Your last step is to move 3 from the left side to the right, changing the sign

    x = -3 +/- {{{sqrt(2)}}}.


The problem is just solved.


<U>ANSWER</U>.  The given equation has two roots  x = -3 + {{{sqrt(2)}}}  and  x = -3 - {{{sqrt(2)}}}.
</pre>


So, &nbsp;we solved the equation by completing the square method.


My congrats, &nbsp;if you learn it for the first time (!)


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