Question

How do you solve `3x^2 -12x = 9` using the quadratic formula?

Answer 1

`x=2+-sqrt7`

Explanation:

`"rearrange terms and equate to zero"`

`rArr3x^2-12x-9=0`

`"divide all terms by 3"`

`rArrx^2-4x-3=0`

`"compare to standard form " ax^2+bx+c=0`

`"here " a=1,b=-4" and " c=-3`

`"using the " color(blue)"quadratic formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(x=(-b+-sqrt((b^2-4ac)))/(2a))color(white)(2/2)|)))`

`rArrx=(-(-4)+-sqrt((-4)^2-(4xx1xx-3)))/(2xx1)`

`color(white)(rArrx)=(4+-sqrt(16+12))/2=(4+-sqrt28)/2`

`color(white)(rArrx)=2+-1/2sqrt28`

`color(white)(rArrx)=2+-1/2sqrt(4xx7)`

`color(white)(rArrx)=2+-sqrt7`