Question

What is an easy way to figure out problems like
x^2-230-21000. Is there an easy way to work these when there are huge numbers? Thank you

Answer 1

your best approach is to use the quadratic formula and a calculator.

with \[x^2-230x-21000\]
we find
\[x= \frac{1}{2}\left( 230\pm \sqrt{230^2+4\cdot21000} \right) \]
you can factor 100 out of the square root, but after that, it is time for the calculator
\[x= \left( 115\pm 5\sqrt{23^2+840} \right)= 115\pm5\sqrt{1369}=115\pm185\]
x= 300 and x= -70

the alternative is to try factors of 21000, various combinations of 3,7, 2^3,5^3
which subtract to give -230. Doable, but...

Answer 2

Thank you