Question 771122
<pre>
2x² - 12x = 7

You didn't divide through by the coefficient of x².
You must do that first:

{{{(2x^2)/2}}}{{{""-""}}}{{{12x/2}}} = {{{7/2}}}

x² - 6x = {{{7/2}}}

Half of -6 is -3.  Square -3, (-3)² = 9,  Add 9 to both sides:

x² - 6x + 9 = {{{7/2}}} + 9

(x-3)(x-3) = {{{7/2}}}{{{""+""}}}{{{18/2}}}

(x - 3)² = {{{25/2}}}

&#8730;<span style="text-decoration: overline">(x - 3)²</span> = {{{"" +- sqrt(25/2)}}}

x - 3 = {{{"" +- sqrt(25/2)}}}

x - 3 = {{{"" +- sqrt(25)/sqrt(2)}}}

x - 3 = {{{"" +- 5/sqrt(2)}}}

x - 3 = {{{"" +- 5/sqrt(2)}}}{{{""*""}}}{{{sqrt(2)/sqrt(2)}}}

x - 3 = {{{"" +- 5sqrt(2)/2}}}

    x = 3  ± {{{5sqrt(2)/2}}} 

    x = {{{6/2}}}  ± {{{5sqrt(2)/2}}}

    x = {{{(6 +- 5sqrt(2))/2}}}

That's the correct answer.
</pre>
 2x^2 - 12x = 7
 2x^2 - 12x + 36 = 43  <--- forgot to divide through by 2
 2(x(x-6) + 18) = 43   <--- shouldn't factor x out of the first two terms
 x(x-6)+ 18 = (43/2)
 x(x-6) = (7/2)
 x^2 - 6x = (7/2)
<pre>
Edwin</pre>