I need help solving this problem using zero-factor property

Question

49x^2+28x+4=0 

Answer 1

in the factored form of ax² + bx + c:

(qx + m)(px + n) = 0, then

m + n = c  and

m * n = b

 

49 is a square of 7, and 4 a square of 2, so let's start there and see how we're shaping up so far:

(7x + 2)(7x + 2) = 0

Just to FOIL back in:

7 * 7 = 49

7 * 2 = 14

2 * 7 = 14

(and 14 + 14 = 28)

2 * 2 = 4

 

So that factorization is indeed correct. Since both factorizations are the same, there is only one place that we're going to be hitting 0, so let's take a look:

7x + 2 = 0

7x = -2

x = -²/₇

 

Answer 2

49x² + 28x + 4 = 0

(7x + 2)² = 0

7x + 2 = 0

7x = -2

x = -2/7

 

{-2/7}

 

The proper name is Zero Product Property.