5x^2=x+1 solve using completion of squares

Take everything to one side and equate it to zero

So: 5x^2 - x - 1=0

Next factorise so it's 5 (x^2-1/5) - 1=0

So: 5 (x-1/5) ^2 - 1=0

So complete the square

First of all remove the five by division (x - ((1/5) / 2) ^2 + (1/5/2) ^2) - 1 = 0

So (x - 1/10) ^2 + 1/5 + 1/100 = 0

Answer is (x-1/10) ^2 - 21/100 = 0

Take - 21/100 to the other side so:

(x-1/10) ^2 = 21/100

Square root both sides so

(X-1/10) = square root of 21/100

Take - 1/10 to the other side so

X = 1/10 + square root of 21/100