Question 1187954
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<pre>

Your starting equation is

    x^2 - 7x - 30 = 0


It is easy to factor:  

    the leading coefficient is 1;

    30 is the product of 3 and 10;  

    you should have it with the " - " sign;

    and  -10  and  3  sum up to  -7,

    so, in factored form, the equation is


    (x-10)*(x+3) = 0.


Obviously, it has the roots  10  and -3.
</pre>

Solved.


I think, &nbsp;the necessary time to get it solved in your head is from &nbsp;10 &nbsp;to &nbsp;20 &nbsp;seconds,

depending on your experience.


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In order for to see many other similar solved problems and to develop your experience, &nbsp;look into my lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Solving-quadratic-equations-without-quadratic-formula.lesson>Solving quadratic equations without quadratic formula</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this textbook under the topic &nbsp;"<U>Quadratic equations</U>". 



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.



Happy learning (!)