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# Completing the square question help

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1. How is completing the square for

m^2-3m+1=0

Supposed to give the answer. 1/2 (3+/-root5). (according to the answer sheet)

My apologies for my keyboard not being able to show certain mathematical symbols +/-
2. (Original post by AnnaClara)
How is completing the square for

m^2-3m+1=0

Supposed to give the answer. 1/2 (3+/-root5). (according to the answer sheet)

My apologies for my keyboard not being able to show certain mathematical symbols +/-
m^2 -3m+1=0
(m-3/2)^2 -9/4 +1 = 0
(m-3/2)^2 = 5/4
(m-3/2) = +/-sqrt(5)/2
m=3/2 +/-sqrt(5)/2
m= 1/2(3+/-sqrt(5))
3. What have you done?

4. then rearrange for m.

It works because if we have
The first part of completing the square gives
, but there's an extra term that is not in the original expression, so you have to subtract the square of the constant;
5. (Original post by ValerieKR)
m^2 -3m+1=0
(m-3/2)^2 -9/4 +1 = 0
(m-3/2)^2 = 5/4
(m-3/2) = +/-sqrt(5)/2
m=3/2 +/-sqrt(5)/2
m= 1/2(3+/-sqrt(5))
How did you get (m-3/2)^2 = +/-sqrt(5)/2 from (m-3/2)^2 = 5/4. ?
6. (Original post by AnnaClara)
How did you get (m-3/2) = +/-sqrt(5)/2 from (m-3/2)^2 = 5/4. ?
square root both sides
7. (Original post by AnnaClara)
How did you get (m-3/2)^2 = +/-sqrt(5)/2 from (m-3/2)^2 = 5/4. ?
8. In this case:

With (if not, then factorise out from whole quadratic), divide by and use in term:

With your example:

Therefore:

Substitute back into your original equation:

Then rearrange to solve for !

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