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

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