The equation 2x2 - 5x = - 12 is rewritten in the form of 2 (x - p) 2 + q = 0. what is the value of q?

2x^2 - 5x + 12 = 0

Factoring out the leading coefficient:

2 (x^2 - 5/2 x) + 12 = 0

Completing the square:

2[ (x - 5/4) ^2 - 25/16] + 12 = 0

2 (x - 5/4) ^2 - 25/8 + 12 = 0

2 (x - 5/4) ^2 + 71/8 = 0

q = 71/8