Question

How do you solve factor `2x^2 +4x-1 = 7x^2 - 7x +1`?

Answer 1

`x=1/5" or "x=2`

Explanation:

`"Rearrange into "color(blue)"standard form"`

`•color(white)(x)ax^2+bx+c=0color(white)(x);a!=0`

`2x^2+4x-1=7x^2-7x+1`

`rArr5x^2-11x+2=0larrcolor(blue)"in standard form"`

`"using the a-c method of factorising"`

`"the factors of + 10 which sum to - 11 are - 10 and - 1"`

`rArr5x^2-10x-x+2=0larrcolor(blue)"split the middle term"`

`rArrcolor(red)(5x)(x-2)color(red)(-1)(x-2)=0larrcolor(blue)"factor by grouping"`

`rArr(x-2)(color(red)(5x-1))=0`

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

`x-2=0rArrx=2`

`5x-1=0rArrx=1/5`