If vector a = (x^2-7, 27) and vector b = (x+3, -9) are parallel vectors in R^2, determine the value(s) of "x".

Vector a = (x^2-7, 27) and vector b = (x+3, -9). The two
vectors a and b are parallel when the coefficients of the x and y components of the
vectors are in the same proportion.

For the same to happen
(x^2 - 7)/(x + 3) = 27/-9

=> -9*(x^2 - 7) = 27*(x +
3)

=> x^2 - 7 = -3(x +
3)

=> x^2 - 7 = -3x -
9

=> x^2 + 3x + 2 =
0

=> x^2 + 2x + x + 2 =
0

=> x(x + 2) + 1(x + 2) =
0

=> (x + 1)(x + 2) =
0

=> x = -1 and x =
-2

The variable x = -1 and x =
-2