Final answer:
To solve the equation 49n^2-7n-2=0 by factoring, we need to find two numbers that multiply to give -98 and add up to -7. The solutions are n=2/7 and n=-1/7.
Step-by-step explanation:
To solve the equation 49n^2-7n-2=0 by factoring, we need to find two numbers that multiply to give -98 (the product of the coefficient of n^2 and the constant term) and add up to -7 (the coefficient of n).
The numbers that satisfy these conditions are -14 and 7.
Therefore, we can rewrite the equation as (7n-2)(7n+1)=0
Setting each factor equal to zero, we get 7n-2=0 and 7n+1=0.
Solving these two equations, we find that n=2/7 or n=-1/7.