Completing The Square

debbie29

New member
Joined
Jul 19, 2005
Messages
14
Hey everyone,

I've been trying to grasp the concept of completing the square, but it still confuses me. I am completely stumped on these two questions. It is probably a stupid mistake I'm making or something-- I just keep getting the wrong answers. Any help/tips would be appreciated.

(1)3x^2-5x-2=0

(2){} = sq rooted
{2x-1} - {x+3}=1

Thanks for your time.
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,486
debbie29 said:
Hey everyone,
I've been trying to grasp the concept of completing the square, but it still confuses me. I am completely stumped on these two questions. It is probably a stupid mistake I'm making or something-- I just keep getting the wrong answers. Any help/tips would be appreciated.
(1)3x^2-5x-2=0

(2){} = sq rooted
{2x-1} - {x+3}=1 Thanks for your time.
What are you asking for?
HOW to complete the square: a classroom session?
Or what the solutions to those 2 problems are?

(1) is fairly simple; factors to:
(3x + 1)(x - 2) = 0
x = -1/3 or x = 2
Do you understand that?

(2) is sqrt(2x - 1) - sqrt(x + 3) = 1
square both sides, then square once more; you'll get:
7x^2 + 30x - 37 = 0; factors to:
(7x + 37)(x - 1) = 0
x = -37/7 or x = 1

So asking again: are you able to solve them not using
complete the square?
 

debbie29

New member
Joined
Jul 19, 2005
Messages
14
They have to be done with completing the square.
Just wanting a walk through for the questions because I can't seem to get them right.
 

ChaoticLlama

Junior Member
Joined
Dec 11, 2004
Messages
199
(1)
3x² - 5x - 2 = 0

First factor out the 3 from the 'x' terms.

3(x² - [5/3]x) - 2 = 0

Now take the coefficient of the x term (in this case, 5/3) and divide it by 2, then square the result.
You will end up with 25/36
To make sure that you do not change the equation (it must remain equal at all times, right?) You both add AND subtract this number from the equation like so.

3(x² - [5/3]x + 25/36 - 25/36) - 2 = 0

Now multiply the term -25/36 by 3 to remove it from the brackets.

3(x² - [5/3]x + 25/36) - 2 - 25/12 = 0

Factor the quadratic.

3(x - 5/6)² - 49/12 = 0

Now just interpret the data.

Therefore the vertex of this parabola is (5/6,-49/12)
 
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