quadratic equation

1)2(x + 1/2)^2 + 10(x + 1/2) + 9 = 0
2(x^2 + x + 1/4) + 10x + 5 + 9 = 0
2x^2 + 2x + 1/2 + 10x + 14 = 0
4x^2 + 4x + 1 + 20x + 28 = 0
4x^2 + 24x + 29 = 0
2.
2x^2+3x-8=0
sum of the roots = A+B = - 3/2
product of the roots = AB = -8/2 = - 4
(A+B)^2 = A^2 + B^2 + 2AB = 9/4
A^2 + B^2 - 8 = 9/4
A^2 + B^2 = 41/4
(A^2 + 1) + (B^2 + 1) = 41/4 + 2 = 49/4
(A^2 + 1)(B^2 + 1) = (AB)^2 + (A^2 + B^2) + 1
= 16 + 41/4 + 1
= 109/4
The require equation is x^2 - (49/4)x + 109/4 = 0
4x^2 - 49x + 109 = 0