Given that the equation x minus 6x + q = 0 to the second power can be reduced to the form of (X-P) square = 7, then what can the square of X - 6x + q = 0 be reduced to kuai

Given that the equation x minus 6x + q = 0 to the second power can be reduced to the form of (X-P) square = 7, then what can the square of X - 6x + q = 0 be reduced to kuai

X ^ 2-6x + q = 0 (1) can be reduced to (X-P) ^ 2 = 7 (2)
By expanding (X-P) ^ 2 = 7, we can get:
x^2-2px+p^2-7=0(3)
Compare (1) and (3). Since (3) is simplified from (1), the two equations should be the same. Then compare the coefficients of the two equations to make the coefficients of the corresponding terms equal
Then:
Quadratic term: 1 = 1 (established)
Linear term: - 2p = - 6 (4)
Constant term: P ^ 2-7 = q (5)
Solution (4) (5) shows that P = 3, q = 2
Then the original equation is:
x^2-6x+2=0
That is, (x-3) ^ 2 = 7
It can be reduced to this formula and its root can be found
x=3±√7