Question

How do you solve `-3x^2+5x=-2`?

Answer 1

`x=-1/3" or "x=2`

Explanation:

`"express in standard form "color(white)(x)ax^2+bx+c=0`

`"add 2 to both sides"`

`rArr-3x^2+5x+2=0`

`"multiply through by "-1`

`rArr3x^2-5x-2=0`

`"using the a-c method to factor"`

`"the factors of the product "3xx-2=-6`

`"which sum to - 5 are - 6 and + 1"`

`"split the middle term using these factors"`

`3x^2-6x+x-2=0larrcolor(blue)"factor by grouping"`

`color(red)(3x)(x-2)color(red)(+1)(x-2)=0`

`"take out the "color(blue)"common factor "(x-2)`

`rArr(x-2)(color(red)(3x+1))=0`

`"equate each factor to zero and solve for x"`

`3x+1=0rArrx=-1/3`

`x-2=0rArrx=2`