Question

How do you solve using the completing the square method `x^2 + 12x + 20 = 0`?

Answer 1

For an in depth explanation of method see
http://socratic.org/s/at7MQHg2

`color(blue)(x~~-1.101" "x~~-10.899)`

Explanation:

Using Shortcuts

Given:`" "y=x^2+12x+12`

Let `k` be the error adjustment constant

`y=x^2+12x+12+k`

Step 1:`" "y=(x^color(magenta)(2)+12x)+12+k`

Step 2:`" "y=(x+color(green)(12)x)^(color(magenta)(2))+12+k`

Step 3:`" use "(1/2)xx(color(green)(12))=color(magenta)(6)`

`=> y=(xcolor(magenta)(+6))^2+12+k`

Step 4:`" "color(magenta)((+6))^2+k=0`

`=>k=color(green)(-36)`

`=>y=(x+6)^2+12-36`

`=>y=(x+6)^2-24`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~

At `y=0"; " x=+- sqrt(24)-6`

`color(blue)(x~~-1.101" "x~~-10.899)`

`color(magenta)("Notice that plots for both equations match")`