Solve by completing the square: 2n^2-n-6=0. Show your work.

n = 2 or n = - 3/2

Step-by-step explanation by completing the square:

Solve for n:

2 n^2 - n - 6 = 0

Divide both sides by 2:

n^2 - n/2 - 3 = 0

Add 3 to both sides:

n^2 - n/2 = 3

Add 1/16 to both sides:

n^2 - n/2 + 1/16 = 49/16

Write the left hand side as a square:

(n - 1/4) ^2 = 49/16

Take the square root of both sides:

n - 1/4 = 7/4 or n - 1/4 = - 7/4

Add 1/4 to both sides:

n = 2 or n - 1/4 = - 7/4

Add 1/4 to both sides:

Answer: n = 2 or n = - 3/2