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

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3