Question

Solve the following equation:
$x^2+|x-1|=1$

Answer 1

$x^2+|x-1|=1$

$|x-1|=1-x^2$

$x-1=1-x^2$

$x^2+x-2=0$

$(x+2)(x-1)=0$

$\therefore x=1$

If $x<1$

$-(x-1)=1-x^2$

$x^2-x=0$

$x(x-1)=0$

$\therefore x=0$

$\therefore x=1$ or $0$