Question

How do you solve using the completing the square method `x^2 + 3x – 6 = 0`?

Answer 1

`x=-3/2+-sqrt33/2`

Explanation:

`x^2+3x=6`

`x^2+2(3/2)xcolor(red)(+9/4)=6color(red)(+9/4)`

`(x+3/2)^2=33/4`

`color(blue)"take the square root of both sides"`

`sqrt((x+3/2)^2)=+-sqrt(33/4)larrcolor(blue)"note plus or minus"`

`x+3/2=+-sqrt33/2`

`"subtract "3/2" from both sides"`

`x=-3/2+-sqrt33/2larrcolor(red)"exact solutions"`

Answer 2

`color(brown)(x = (-1/2) (3 - sqrt33 ), -(1/2) ( 3 + sqrt33)`

Explanation:

`x^2 + 3x - 6 = 0`

`x^2 + 3x + (3/2)^2 - 6 = (3/2)^2, "adding " (3/2)^2 " to both sides"`

`x^2 + 2 * 3/2 * x + (3/2)^2 = (3/2)^2 + 6`

`(x + 3/2)^2 = 33/4`

`(x + 3/2)^2 = (sqrt(33/4))^2`

`x + 3/2 = +- sqrt(33/4), " taking squre root on both sides"`

`x = -3/2 +- sqrt33 / 2`

`color(brown)(x = (-1/2) (3 - sqrt33 ), -(1/2) ( 3 + sqrt33)`