# How do you solve using the completing the square method #x^2 - 5x = 9#?

##### 1 Answer

Take the coefficient of the

1. Divide it by 2 (to get

2. Square this (to get

3. Add this final value to both sides.

#### Explanation:

Completing the square means seeking a constant term

First, let's look at what happens when we FOIL a perfect square binomial of the form

#(x+a)(x+a)=x^2+2ax+a^2#

A perfect square will always have a distributed form like this.

What we notice is that if we take the coefficient of the

#x^2+2ax+a^2 = b + a^2#

so that the trinomial on the left will be guaranteed to be a perfect square—the square of

For this particular problem, we are given

#-5=2a# ,

then

#a=-5/2# ,

and

#a^2=25/4# .

Thus,

#x^2-5x+25/4=9+25/4#

Okay, so if this

That's easy—remember that the factored form of *half* of the *half* of

We simplify both sides now to get

#(x-5/2)^2=61/4#

Now our LHS is a perfect square, so we can solve for

#x-5/2=+-sqrt61 /2#

and then adding

#x=5/2+-sqrt61 / 2" "=" "(5+-sqrt61)/2# .

## Note:

If the coefficient on the