# Complete the square - Help please

1. Oct 19, 2004

### iNsChris

Complete the square - Help please :)

Not to good with fractions, so i'm posting this here.

x^2 + 3x +4

Complete the square.

Ill try:

(x + 3/6)^2 + ?

lol best i can do sorry :)

Thanks

2. Oct 19, 2004

### The Bob

x^2 + 3x + 4
=> (x + 1.5)^2 +4 - 2.25
=> (x + 1.5)^2 +1.75

There you go.

3. Oct 19, 2004

### iNsChris

yeh i considered decimals but book showed fractions - Cheers mate.

4. Oct 19, 2004

### cepheid

Staff Emeritus
What is that supposed to mean? It makes no difference how you express the numbers (every fraction has some decimal representation!), the method of solving the problem is always the same.

$$x^2 + 3x +4 = \left(x + \frac{3}{2}\right)^2 + 4 - \left(\frac{3}{2}\right)^2$$

Do you see the general procedure for completing the square? It's always the same. Think about what it means to "complete the square". We want to add 'something' to the expression so that we end up with a perfect square. (and then subtract that same 'something' so that in the end we haven't changed anything). i.e. so that

x^2 + 3x + something + 4 - something

can be expressed using the square of some binomial (ie so that the italicized part is a perfect square):

= (x + ?)^2 +4 - something

Can you see that '?' must be half of 3 in this case? -- because when you expand, you get x^2 + 2?x + ?^2
so (2? = 3)

It follows that 'something' = ?^2 = (3/2)^2 = 9/4

So if you understand and follow this reasoning every single time, completing the square will never be any trouble.

btw last time I checked:

3/2 = 1.5

9/4 = 2.25

5. Oct 19, 2004

### misogynisticfeminist

for the function, actually there's an easier way to complete the square, just simply expand it out, what i mean is

$$x^3+3x+4=a(x+b)^2+c$$

equate these 2 together, expand out $$a(x+b)^2+c$$ then compare the coefficients.

6. Oct 19, 2004

### The Bob

I believe Chris understands this but thought that he had to use fractions when really decimals were alright.

The completing the square process is simple and he has it but it was a little doubt that needed sorting.