Question 185227
2x^2-24x+33=0
<pre>

First you try to factor it:

Multiply 2 by 33, getting 66.  Now we make a column of
ways to factor 66 using two integers:

factors
 1x66
 2x33
 3x22
 6x11


Now since the sign of 66 is positive, we make
a list of the sums:

<pre>
factors      sums of factors
 1x66          1+66=67    
 2x33          2+33=35 
 3x22          3+22=25
 6x11          6+11=17
</pre>
Now you try to find one that agrees in absolute value
with the middle term of 

2x^2-24x+33=0

Oh oh!  There aren't any!  So it won't factor. So we 
have to use the quadratic formula.

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

a=2, b=-24, c=33

{{{x = (-(-24) +- sqrt( (-24)^2-4*(2)*(33) ))/(2*(2)) }}}

{{{x = (24 +- sqrt( 576-264 ))/(4) }}}


{{{x = (24 +- sqrt( 576-264 ))/(4) }}}


{{{x = (24 +- sqrt(312))/4 }}}

{{{x = (24 +- sqrt(4*78))/4 }}}

{{{x = (24 +- 2sqrt(78))/4 }}}

Factor 2 out of the top

{{{x = (2(12 +- sqrt(78)))/4 }}}

Divide top and bottom by 2:

{{{x = (12 +- sqrt(78))/2 }}} 
Edwin</pre>