
reducing quadratic
hello, I have this quadratic:
180x^2 + 12000x  100000
What is the best way of reducing this down as much as possible so I more easily solve it ?
I see I could factor out 20 eg. 20(90x^2 + 600x  5000), but is there a more effective way of reducing it ?
thanks for any help.

Re: reducing quadratic
Why not take out another factor of 10?

Re: reducing quadratic
$\displaystyle 180x^2+12000x100000$
Take out a factor of 180
$\displaystyle = 180\left (x^2\frac{12000}{180}x+\frac{100000}{180} \right)$
$\displaystyle = 180\left (x^2\frac{200}{3}x+\frac{5000}{9} \right)$
$\displaystyle = 180\left (x^2\frac{200}{3}x+\frac{5000}{9} +\frac{40000}{36}\frac{40000}{36}\right)$
$\displaystyle = 180\left( \frac{36x^224000x+40000}{36}\frac{20000}{36}\right)$
$\displaystyle = 180\left[ \left(\frac{6x200}{6}\right)^2\left(\frac{100\sqrt{2}}{6}\right)^2 \right]$
Now, use difference of squares to factorize the expression.