Question

What is the solution set of the following equation? 4/5 x2 = 2x - 4/5

Answer 1

`x=(1)/(2)` or
`x=2`

Explanation:

The given quadratic equation is:

`(4)/(5)x^2=2x-(4)/(5)`

We multiply through by 5 to get:

`4x^2=10x-4`

Rewrite in standard quadratic form;

`4x^2-10x+4=0`

Or

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

Split the middle term to get:

`2x^2-4x-x+2=0`

Factor to get:

`2x(x-2)-1(x-2)=0`

Factor further to get:

`(2x-1)(x-2)=0`

Either
`(2x-1)=0` or
`(x-2)=0`

Either
`x=(1)/(2)` or
`x=2`