Find the solutions to the equation below check all that apply

2x^2+7x+3=0

A. x=2

B. x=7

C. x=-1/2

D. x=3

E. x=4

F. x=-3

2x^2+7x+3=0: x=-1/2 and x=-3 c and F

C. x=-1/2 and F. x=-3

Step-by-step explanation:

We can solve this by factoring. We will look for factors of a*c, 2*3, that sum to b, 7. Factors of 6 are:

1 and 6; these sum to 7.

2 and 3; these do not sum to 7.

We will use 1 and 6. We will split bx, 7x, into 1x and 6x:

2x²+1x+6x+3 = 0

We will group the first two and the last two terms together:

(2x²+1x) + (6x+3) = 0

We will factor out the GCF of each group. The GCF of the first group is 1x:

1x (2x+1) + (6x+3) = 0

The GCF of the second group is 3:

1x (2x+1) + 3 (2x+1) = 0

The GCF of the two terms remaining is (2x+1); factoring this out,

(2x+1) (1x+3) = 0

Using the zero product property,

2x+1 = 0 or 1x+3 = 0

To solve the first equation, subtract 1 from each side:

2x+1-1 = 0-1

2x = - 1

Divide both sides by 2:

2x/2 = - 1/2

x = - 1/2

To solve the second equation, subtract 3 from each side:

1x+3-3 = 0-3

x = - 3