Question 608704
3x² + 7x = 12
<pre>
So you asked if that becomes:  x² + {{{7/4}}}x = 4?
No because the first step is to divide through by the
coefficient of x², which is 3. And we divide all the terms,
on both sides by 3 

{{{3/3}}}x² + {{{7/3}}}x = {{{12/3}}}

           x² + {{{7/3}}}x = 4 

 So {{{7/4}}} has the wrong enominator.

But it seems a shame to stop here and not go on and
complete the square.  Let's do it just for fun:
(You can print it for future use, because you're
going to have to learn how to do that soon.
 

multiply {{{1/2}}} times {{{7/3}}}, get {{{7/6}}}
Square {{{7/6}}}. get {{{49/36}}}

Add that to BOTH sides of the equation, to keep
it balanced.
  
So now we have:

x² + {{{7/3}}}x+{{{49/36}}} = 4+{{{49/36}}}

That factors as:

(x + {{{7/6}}})² = {{{193/36}}}

Now we use the principle of square roots:

 x + {{{7/6}}} = {{{"" +- sqrt(193/36)}}}
 
 x + {{{7/6}}} = {{{"" +- sqrt(193)/6)}}}

             x = {{{-7/6 +- sqrt(193)/6)}}}

             x = {{{(-7 +- sqrt(193))/6}}}

Edwin</pre>