Question

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

Answer 1

Answer:

$x=\frac{1}{2}$ or $x=2$

Step-by-step explanation:

The given quadratic equation is:

$\frac{4}{5}x^2=2x-\frac{4}{5}$

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 $x=\frac{1}{2}$ or $x=2$