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

[Mphisto]

Homework Statement

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

Homework Equations

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
Please check my answer and correct me

Thank you!

 

[Mentallic]

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

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

 

[Mphisto]

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

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

 

[Mentallic]

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

Yep that's better!