Algebra

Complete the square: x^2 - 10x + 21 + 3x^2 - 2x + 8.     

                                    x² – 10x + 21 + 3x² – 2x + 8     

first, combine like terms so     

you can see what you've got        4x² – 12x + 29     

"semi-factor" it, set it up so     

you can see what you need          (2x –  n  )(2x –  n  )     

(2 • n • 2x) has to be 12x      

so n = 3                                          (2x – 3)(2x  – 3)     

by itself, that works out to               4x² – 12x + 9     

but it was 29 and that     

other 20 has to come     

from somewhere... add it                4x² – 12x + 9 + 20          

so you end up with                          (2x – 3)² + 20     

I think.  I'm not accustomed to completing the square     

without an equals sign making it part of an equation.     

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