How do you solve using the completing the square method $a²-a-1=0$ ?

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Answer 1 · 2016-03-21T01:07:26

$a=(1+-sqrt(5))/2$

First multiply the whole equation by $2^2=4$ to cut down on the fractions involved.

$0 = 4a^2-4a-4$

$= 4a^2-4a+1-5$

$= (2a-1)^2-(sqrt(5))^2$

$= ((2a-1)-sqrt(5))((2a-1)+sqrt(5))$

$= (2a-1-sqrt(5))(2a-1+sqrt(5))$

Hence:

$a=(1+-sqrt(5))/2$

How do you solve using the completing the square method a²-a-1=0a²-a-1=0?