hello.
i have got this one algebra question for homework.
however i had no idea on how to do this attached one.
i need to find answers for both a= and b=.
One way is to expand the righthand side, then match its terms to those of the lefthand side.
x^2 +6x -3 = (x+a)^2 +b
x^2 +6x -3 = (x^2 +2ax +a^2) +b
x^2 +6x -3 = x^2 +2ax +a^2 +b
x^2 +6x -3 = x^2 +2ax +(a^2 +b)
So,
x^2 = x^2 ----(i)
6x = 2ax -----(ii)
-3 = (a^2 +b) -----(iii)
From (ii),
6 = 2a
a = 6/2 = 3 ----***
Substitute that into (iii),
-3 = (3)^2 +b
-3 = 9 +b
-3 -9 = b
b = -12 ---***
Check those in the original equation,
x^2 +6x -3 = (x+a)^2 +b
x^2 +6x -3 =? (x+3)^2 +(-12)
x^2 +6x -3 =? (x^2 +6x +9) -12
x^2 +6x -3 =? x^2 +6x +9 -12
x^2 +6x -3 =? x^2 +6x -3
Yes, so, OK
Therefore, a = 3 and b = -12. -------answer.