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

Question

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

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Answer 1 · 2017-03-13T07:18:24

#a=64# and #b=-8#

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 · 2017-03-13T07:20:25

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

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#