Question

Solve the equation 2x^2-x=1

Answer 1

First move all terms to the same side.
2x^2-x-1=0
Factor this to get
(2x+1)(x-1)=0
Separate into
2x+1=0 and x-1=0
Solve these two to get
X=-1/2 or x=1
Final answer:
X=-1/2 or x=1

Answer 2

$2x^2-x=1\ \ \ | subtract\ 1\\\\ 2x^2-x-1=0\\\\use\ factorization:\\ write\ -x\ as\ x-2x\\\\ 2x^2+x-2x-1=0\\\\ x(2x+1)-1(2x-1)=0\\\\ (x-1)(2x+1)=0\\\\ x=1\ \ \ or\ \ \ 2x=-1\\\\ x=1\ \ \ or \ \ \ x=-\frac{1}{2}$