Factor completely into primes

Question

V₀²+V₀+0.25

Answer 1

Factors of 1/4 that add up to 1.

 

we see 1/2*1/2 = 1/4 and 1/2+1/2 = 1.

 

hence 

v^2+v+1/4 = (v+1/2)(v+1/2)