Algebra: Quadratics - Completing the Square

Worked Solution:

( c + a )² = c² + 2 a c + a²
( c + a )² + b = c² + 2 a c + a² + b
We want to find values for a and b to make the line above into c² – 6 c – 7
We already have the c² term so let's look at the c term:

2a c =

–6

c :

For the quadratic in the question, the c coefficient is

–6

which must be equal to the c term above:

2 a =

–6

a =

–3

a2 + b =

–7

: The quadratic given has a constant term of

–7

This must equal a2 + b and we now know the value of a =

–3

a2 =

9

:

9

+ b =

–7

b = –16