Question

How do you solve using the completing the square method `3x^2-7x-6=0`?

Answer 1

`color(green)(x=3)` or `color(green)(x=-2/3)`
`color(white)("XXX")`see below for solution method using "completing the square"

Explanation:

`3x^2-7x-6=0`
`rArrcolor(white)("XXX")color(blue)(x^2-7/3x)=color(blue)2`

If `x^2-7/3x` are the first two terms of a squared binomial:
`color(white)("XXX")(x+a)^2=x^2+2ax+a^2`
then
`color(white)("XXX")2a=-7/3color(white)("X")rarrcolor(white)("X")a=-7/6`
and to "complete the square" we will need to add
`color(white)("XXX")color(red)(a^2)=(-7/6)^2=color(red)(49/36)`

giving:
`color(white)("XXX")color(blue)(x^2-7/6x)color(red)(+49/36)=color(blue)2color(red)(+49/36)`

`rArrcolor(white)("XXX")(x-7/6)^2= (2xx36+49)/36=121/36= (11/6)^2`

`rArrcolor(white)("XXX")x-7/6=+-11/6`

`rArrcolor(white)("XXX")x=(7+-11)/6`

`rArrcolor(white)("XXX")x=18/6=3color(white)("X")orcolor(white)("X")x=-4/6=-2/3`