5m^2+12m+6=0 complete the square

Question

complete the square

Answer 1

separate the first two terms on the left and factor out 5

5(m² + (12/5)m ) + 6 = 0

take half the middle coefficient (12/5), square it, and add it to the terms in parentheses

5(m² + (12/5)m + 36/25) + 6 = 0 + 36/5 (this has the effect of adding 36/5 to both sides)

simplify and rearrange:

5(m + 6/5)² = 6/5 ===> (m+6/5)² = 6/25

square root both sides:

m+6/5 = ±√6/5

m = (-6+√6)/5 or m = (-6-√6)/5