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:

n = 2 or n = -3/2

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

(x+3)(x+7)

step-by-step explanation: