Quadratic equation

[Ruben]

Hi,

What number must be added to x2 - 9x to complete the square?



I have the answer but I don't anderstand it!

http://www.lavc.cc.ca.us/math/samples/i ... index.html

[RA]

I am assuming you meant: x^2 - 9x

Quadratic equations generally have 2 solutions (a & b) and can be represented as (x+a) (x+b). If the equation is a square then it would have a single solution (a=b) and can be represented as (x + a)^2.

As per the rules of quadratic equation factorization:
2a = - 9
a = - 9/2.

Again the rules of factorization the constant term that needs to be added to the equation is a^2
a^ 2= (-9/2)^2 = 81/4

Hence the answer is 81/4.

Hope that helps

[RonPurewal]

the rule is: take the coefficient of x, divide it in half, and then square the resulting number.

here the coefficient of x is -9 (although you can ignore the negative sign, since you're eventually going to square the number anyway - the complete-the-square term will turn out positive no matter what).
cutting that in half yields -9/2
squaring yields 81/4

then you have x^2 - 9x + 81/4, which will factor to (x - 9/2)^2. note that this factorization would be difficult to find at random, but you aren't finding it at random; you already know ahead of time that the expression will factor into a perfect square (hence the expression "completing the square"), and therefore the factorization is easy to find.