Question

How do you solve `2x^2+11x+5=0`?

Answer 1

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

Explanation:

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

`"consider the factors of the product "2xx5=10`
`"which sum to + 11"`

`"the required factors are + 10 and + 1"`

`"split the middle term using these factors"`

`2x^2+10x+x+5=0larrcolor(blue)"factor in groups"`

`rArrcolor(red)(2x)(x+5)color(red)(+1)(x+5)=0`

`"take out the common factor "(x+5)`

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

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

`x+5=0rArrx=-5`

`2x+1=0rArrx=-1/2`