Can you complete this quadratic equation? Algebra 2

Equation: x2 + 8x + 12 = 0

Worded: x squared plus eight x plus twelve equals zero.

There is a twist: Do this by

-Factoring (Demonstrate how to solve your equation by factoring)
-Completing the Square (demonstrate how to solve your equation by completing the square)
-The Quad Formula (demonstrate how to solve the equation using the quadratic formula)

And that's it.

x^2 + 8x + 12 = 0

First by factoring:

(x + 6) * (x + 2) = 0

So, x = -6 and x = -2


Next, by completing the square, first move the 12 over

x^2 + 8x = -12

Divide 8 in half to get 4, square it to get 16, and add this to each side:

x^2 + 8x + 16 = 4

Factor to find the squared term:

(x + 4)^2 = 4

Square root (remembering both roots):

x + 4 = 2 and x = 4 = -2

Solving for x:

x = -2 and x = -6


By the quadratic formula, using a = 1, b = 8, and c = 12:

-8 +/- sqrt((8)^2 - 4(1)(12)) / 2(1)

-8 +/- sqrt(64 - 48) / 2

-8 +/- sqrt(16) / 2

The two solutions are:

x = (-8 + 4)/2 and x = (-8 - 4)/2, which are:

x = -2 and x = -6

Factoring:

(x + 6)(x + 2)=0

So, by the zero factor property: x + 6 = 0 and x + 2 = 0. Which means x = -6 and x = -2.

Completing the square:

Get the x-terms on one side

x2 + 8x = -12

Add (8/2)^2 to both sides to complete the square on the left side. (8/2)^2 = (4)^2 = 16

x2 + 8x + 16 = -12 + 16

(x + 4)^2 = 4

Take the square root of both sides to get

x + 4 = +-2

This gives x = -4 +- 2, which means x = -4 + 2 and x = -4 - 2, which means x = -2 and x = -6

The Quad Formula:

A = 1, B = 8 and C = 12, so

x =[ -8 +- squareroot(8^2 - 4*1*12)] / 2(1)

x = [-8 +- squareroot(64 - 48)] / 2

x = [-8 +- 4] / 2

So, x = -12/2 = -6 and x = -4/2 = -2

Factoring: (x+6)(x+2)
x=-6,-2

Completing the square:
x^2 + 8x = -12
Take half of 8, 4. Square it and add it to both sides
x^2 + 8x +16 = -12+16
(x+4)(x+4)=4
Squre root both sides
x+4=+/- 2
x=-4 +/- 2
x=-6,-2

Quad Formula:
a=1
b=8
c=12
-8 +/- Sqroot (8^2-(4*1*12))/2(1)
-8 +/- Sqroot (64-48)/2
-8 +/- Sqroot (16)/2
(-8 +/- 4)/2
-8+4=-4/2=-2
-8-4=-12/2=-6