Question

I RLLY NEED HELP PLS!!

Answer 1

Answer:  $(x+2)^2+3$

a = 2 and b = 3

==================================================

Explanation:

Let's expand out $(x+a)^2+b$ to get the following:

$(x+a)^2+b\\\\(x+a)(x+a)+b\\\\x(x+a)+a(x+a)+b\\\\x^2+ax+ax+a^2+b\\\\x^2+2ax+a^2+b$

The x term here is 2ax

Compare this to the x term of $x^2+4x+7$ and we see that

$2ax = 4x\\\\2a = 4\\\\a = 4/2\\\\a = 2$

--------------

The constant term of $x^2+2ax+a^2+b$ is the $a^2+b$ portion since it doesn't have the variable x attached to it.

Compare this with the 7 of $x^2+4x+7$ which is also the constant.

Equate the two items, plug in a = 2 and solve for b.

$a^2+b = 7\\\\2^2+b = 7\\\\4+b = 7\\\\b = 7-4\\\\b = 3$

Therefore,

$x^2+4x+7 = (x+a)^2+b\\\\x^2+4x+7 = (x+2)^2+3$