Solve 2x2 + 5x = 12.

A. x = three over two and x = - 4

B. x = 2 and x = - 3

C. x = - 6 and x = 5

D. x = one over two and x = one over three

A. x = three over two and x = - 4

Step-by-step explanation:

2x^2 + 5x = 12

I will use complete the square

Divide each side by 2

2x^2 / 2 + 5/2 x = 12/2

x^2 + 5/2 x = 6

Take 5/2, divide by 2 and then square it

5/2 : 2 = 5/2 (5/4) ^2 = 25/16

Add this to both sides

x^2 + 5/2 x + 25/16 = 6 + 25/16

(x+5/4) ^2 = 6 * 16/16 + 25/16

(x+5/4) ^2 = 96/16 + 25/16

(x+5/4) ^2 = 121/16

Take the square root of each side

sqrt ((x+5/4) ^2) = sqrt (121/16)

x+5/4 = ±11/4

Subtract 5/4 from each side

x+5/4-5/4 = ±11/4 - 5/4

x = ±11/4 - 5/4

x = - 11/4 - 5/4 and x = 11/4 - 5/4

x = - 16/4 = - 4 and x = 6/4 = 3/2