Question

How do you solve using the completing the square method `0=3x^2-2x-12`?

Answer 1

`x=1/3+-sqrt37/3`

Explanation:

`"require the coefficient of " x^2" term to be unity"`

`rArr3(x^2-2/3x-4)=0`

`"to complete the square"`

add `(1/2"coefficient of the x-term")^2" to " x^2-2/3x`

`3(x^2-2/3xcolor(red)(+1/9)color(magenta)(-1/9)-4)=0`

`"we must also subtract " 1/9`

`rArr3((x-1/3)^2-37/9)=0`

`"distributing gives"`

`3(x-1/3)^2-37/3=0`

`rArr(x-1/3)^2=37/9`

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

`rArrx-1/3=+-sqrt(37/9)larr" note plus or minus"`

`"add "1/3" to both sides"`

`rArrx=1/3+-sqrt37/3`