Question

solve 3x^2+18x+15=0 by completing the square

Answer 1

@surjithayer

Answer 2

@AccessDenied

Answer 3

hm

Answer 4

do you know what a perfect square trinomial is?

Answer 5

1.take common 3
2.add the square of half the co-efficient of x.

Answer 6

im confused

Answer 7

\[3\left( x^2+6x \right)+5=0,3\left( x^2+6x+9-9 \right)+5=0\]
\[3\left( x^2+6x+9 \right)-27+5=0\]
\[3\left( x+3 \right)^2-22=0\]
\[\left( x+3 \right)^2=\frac{ 22 }{ 3 },x+3=\pm \sqrt{\frac{ 22 }{ 3 }}\]
find x

Answer 8

im still confused

Answer 9

solve 3x^2+18x+15=0 by completing the square:

Let's go thru this quickly, with your involvement. Later, we could discuss the why's.

3 is a factor common to all four terms in 3x^2+18x+15=0.
Please factor out the 3 right now:

3( ??? )

Answer 10

15/3 = ?

Answer 11

15 x 3 or 15 divided by 3?

Answer 12

I was just trying to help you get started on the necessary factoring.\[\frac{ 15 }{ 3 }=?\]

Answer 13

5

Answer 14

Right. and (3x^2)/3 = ?

Answer 15

3?

Answer 16

\[\frac{ 3x^2 }{ 3 }=?\]Hint: just cancel the 3s.

Answer 17

x^2

Answer 18

Right. and \[\frac{ 18x }{ 3 }=?\]

Answer 19

6

Answer 20

Actually, that'd be 6x.

Then 3x^2+18x+15=0 has been factored: 3(x^2 + 6x +5)=0.
Look carefully. Does this make sense to you?

Answer 21

yes

Answer 22

Great.
Now, we're going to ignore that coefficient 3 for a while, and focus only on
x^2 + 6x +5.

We're going to do something to x^2 + 6x + 5 called "completing the square."
I won't explain a lot right now, but rather will just ask you to do this or that; we'll go into the reasons later if you're interested.

Answer 23

Re-write x^2 + 6x + 5 as x^2 + 6x + 5
Now take the coefficient of x (which is 6); halve it.
What do you get?
Half of 6 is what?

Answer 24

3

Answer 25

Good. Now please square that 3. 3^2 = ?

Answer 26

9

Answer 27

Right you are!

Now take another look at

x^2 + 6x + 5

Add your 9 to the right of the 6x term; then subtract 9 from the 1st 9.

Answer 28

huh?