Question

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

Answer 1

A. x= three over two and x = −4

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