Question

How to find the value of a and the value of b?

`x^2-16x+a=(x+b)^2`

Answer 1

`a=64` and `b=-8`

Explanation:

This appears to be a way of finding a number `a`, which when added to `x^2-16x` results in a square of form `(x+b)^2`

We can write `x^2-16x+a=(x+b)^2` as

`x^2-16x+a=x^2+2bx+b^2`

Now comparing coefficients of similar terms

`2b=-16` or `b=-8`

and `a=b^2=(-8)^2=64`

Answer 2

`a=64" "` and `" "b=-8`

Explanation:

Given:

`x^2-16x+a = (x+b)^2`

`color(white)(x^2-16x+a) = x^2+2bx+b^2`

Equating the coefficients of `x`, we find:

`-16 = 2b`

Hence:

`b = -8`

Then:

`b^2 = (-8)^2 = 64`

So equating the constant terms, we find:

`a = 64`