X2-6x+3 can be written in the form of (x+m)2 +n find the value of m and n

m = - 3, n = - 6

Step-by-step explanation:

Expand and compare coefficients of like terms, that is

(x + m)² + n

= x² + 2mx + m² + n

Compare to x² - 6x + 3

comparing coefficients of x- term

2m = - 6 ( divide both sides by 2 )

m = - 3

Comparing constant terms

m² + n = 3 , that is

(- 3)² + n = 3

9 + n = 3 ( subtract 9 from both sides )

n = - 6

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: