Question 528491
<pre>
x² + {{{3/2}}}x = 3

Multiply the coefficient of x, which is {{{3/2}}} by {{{1/2}}}, getting {{{3/4}}}.
Now square {{{3/4}}}, getting {{{(3/4)^2}}} = {{{9/16}}}

Add +{{{9/16}}} to both sides of the equation:

x² + {{{3/2}}}x + {{{9/16}}} = 3 + {{{9/16}}}

The left side will now factor as (x + {{{3/4}}})(x + {{{3/4}}}) or (x + {{{3/4}}})².  So we have:

(x + {{{3/4}}})² = 3 + {{{9/16}}}

We will combine the terms on the right by getting the LCD of 16.
Then 3 + {{{9/16}}} becomes {{{48/16}}} + {{{9/16}}} or {{{57/16}}}.
So we now have:

(x + {{{3/4}}})² = {{{57/16}}}

Next we use the principle of square roots:

x + {{{3/4}}} = ±{{{sqrt(57/16)}}}

x + {{{3/4}}} = ±{{{sqrt(57)/4)}}}

Solve for x by adding {{{-3/4}}} to both sides:

      x = {{{-3/4}}} ± {{{sqrt(57)/4)}}}

or you can write it:

      x = {{{(-3 +- sqrt(57))/4}}}

Edwin</pre>