solve the equation 2x^2-x=1
\(2x^2-x=1\ \ \ | subtract\ 1\\\\ 2x^2-x-1=0\\\\use\ factorization:\\ write\ -x\ as\ x-2x\\\\ 2x^2+x-2x-1=0\\\\ x(2x+1)-1(2x-1)=0\\\\ (x-1)(2x+1)=0\\\\ x=1\ \ \ or\ \ \ 2x=-1\\\\ x=1\ \ \ or \ \ \ x=-\frac{1}{2}\)
First move all terms to the same side. 2x^2-x-1=0Factor this to get (2x+1)(x-1)=0Separate into2x+1=0 and x-1=0Solve these two to get X=-1/2 or x=1Final answer:X=-1/2 or x=1
