Answer:
p = 3 and q = 7
Explanation:
Given the equation x^2 + 6 x − 2 = ( x + p )^2 + q we are to find the value of p and the value of q .
x^2 + 6 x − 2 = ( x + p )^2 + q
Using the completing the square method on x^2 + 6 x − 2
x^2 + 6 x − 2
= x^2+6x+ 9 - 2 + 9
= (x^2+3x+3x+9)+7
= x(x+3)+3(x+3) + 7
= (x+3)(x+3)+7
= (x+3)^2+7
Compare to the right hand side
(x+3)^2+7 = ( x + p )^2 + q
p = 3 and q = 7