x²-x+1=7用十字相乘法解答一下,需要具体过程

x²-x+1=7
x^2-x-6=0
x - a
* x - b
-------------------------------
-bx + ab
+ x^2 -ax
-------------------------------
x^2-(a+b)x+ab = x^2-x-6 =(x-3)(x+2)=0 x1=3,x2=-2
a+b=1 ab=-6 a=3 b=-2