How do you complete the square to solve a quadratic equation?

Question

amistre64 · Answer

first understand what a square is :)

anonymous · Answer

A good website :D http://www.mathsisfun.com/algebra/completing-square.html

amistre64 · Answer

given an equation like:  x^2 + 6x + ___  what do we do to "complete the square"?

\begin{array}c
&&&(6/2)x\         
&x^2&x&x&x\
&x\
(6/2)x&x\
&x\
\end{array}

how many parts do we nee to fill in to make a "complete square?


\begin{array}c
&&&(6/2)x\         
&x^2&x&x&x\
&x&1&2&3\
(6/2)x&x&4&5&6\
&x&7&8&9\
\end{array}

9 parts :)

x^2 + 6x + 9  is a complete square

amistre64 · Answer

this is fun for simple geometric equivalences, but can get messy, so we simply stick the the algebra

given an equation:  ax^2 +bx + ___

we can "complete the square" by adding (b/2)^2 to it

amistre64 · Answer

x^2 + 4x + ___

(4/2)^2 = 2^2 = 4

x^2 + 4x + 4 is a complete square

amistre64 · Answer

x^2 - 5x + ____

(5/2)^2 = 25/4

x^2 - 5x + 25/4  is a complete square

amistre64 · Answer

once you know a complete square, it can be compressed, or compacted.

x^2 + bx + (b/2)^2 = (x+(b/2))^2

anonymous · Answer

Thanks amistre64. I'm 69 years old and brushing up on precalc/calc to help my 16 year old daughter. I asked the question to see if this forum really works, but your answer also helps me REMEMBER how to do the algebra here. Thanks again.

amistre64 · Answer

youre welcome, im abt 40 and still brushing up :)

amistre64 · Answer

there is a hodgepodge of answerers here, and if you need an indepth answer, dont be afraid to ask