Question 541006
Step 1: Factor out -1 to make the X side look normal
{{{y=(-1)(x^2-4x+1)}}}
Step 2: Factor the quadratic - which you can't do as is. You need to adjust it and make it workable. Although {{{X^2-4X+1}}} isn't factorable, {{{X^2-4x+4}}} is. So both add and subtract 4 from the right hand side, but don't reduce. Simultaneously adding and subtracting 4 is a net change of zero, so the equation will still balance.
{{{y=(-1)(x^2-4x+4-4+1)}}}
Step 3: Factor the quadratic, and reduce.
{{{x^2-4x+4=(x-2)^2}}}
So {{{y=(-1)(x^2-4x+4-4+1)}}} becomes
{{{y=(-1)((x-2)^2-3)}}}
{{{y=-(x-2)^2+3}}}
Step 4: Set y=0 and solve for x
{{{y=-(x-2)^2+3}}}
{{{0=-(x-2)^2+3}}}
{{{-3=-(x-2)^2}}}
{{{3=(x-2)^2}}}
{{{sqrt(3)=x-2}}} and {{{sqrt(3)=-x+2}}}
{{{x=2+-sqrt(3)}}}