3x^2 - 5x - 1 = 0 (Solve using completing the square method)

1. Jan 29, 2012

Mphisto

1. The problem statement, all variables and given/known data
Question: 3x^2 - 5x - 1 = 0 (Solve using completing the square method)

2. Relevant equations

3. The attempt at a solution
3x^2 - 5x - 1 = 0
x^2 - (5/3)x - 1/3 = 0
x^2 - (5x/3) = 1/3
x^2 - 2(5x/3) = 1/3
x^2 - 2(5x/3) + (5/6)^2 = 1/3 + (5/6)^2
(x - 5/6)^2 = 1/3 + 25/36
(x - 5/6)^2 = 37/36
x - 5/6 = + - Square root 37/36
x = Square root 37/36 + 5/6 or x = - Square root 37/36 + 5/6
x = 1.85 (3sf) or x = -0.180 (3sf)

I am sorry if the working is messy! I can't find the appropriate key for it

Thank you!!!!!

2. Jan 29, 2012

Mentallic

How did you get from the first to the second? What you basically said here is that if

$a+b=c$

then

$a+2b=c$

This is not true unless b=0, which is not the case. What you should have instead done is

$a+b=c$

then

$a+2(\frac{b}{2})=c$

Notice here that nothing has changed, so the equality still holds.

Everything else seems good and you have the correct answer

3. Jan 29, 2012

Mphisto

Thanks for taking the time to check!

Edit: It should has been x^2 - 2(5x/6) = 1/3
x^2 - 2(5x/6) + (5/6)^2 = 1/3 + (5/6)^2

4. Jan 29, 2012

Mentallic

Yep that's better!