Question 598027
<pre>
y = x² - 10x + 8

Multiply coefficient of x, which is -10, by {{{1/2}}}, getting -5.
Square -5, getting (-5)² = +25.

Add 25 - 25 (which is really zero) to the right side after the -10x

y = x² - 10x + 25 - 25 + 8

Factor the first three terms on the right sides:

y = (x - 5)(x - 5) - 25 + 8

Write (x - 5)(x - 5) as (x - 5)², and write -25 + 8 as -17

y = (x - 5)² - 17

That's it.

Edwin</pre>