Question

COMPLETE THE SQUARE

Answer 1

X^2-10X+27

Answer 2

do you know what a "perfect square trinomial" is?

Answer 3

NO

Answer 4

ok so a perfect square trinomial, so-called is really just a binomial of second degree
that is \(\bf (a\pm b)^2\)

now keep in mind that \(\bf (a\pm b)^2 = a^2\pm 2ab+b^2\)

Answer 5

ok

Answer 6

the plus/minus is not required since the terms are general to begin with

Answer 7

so as an example if I had say
\(\bf 4x^2+ 12xy + 9y^2\)
is really equals to
\(\bf (2x)^2 + 2(2x)(3y) + (3y)^2 \implies (2x+3y)^2\)

Answer 8

$$\bf x^2-10x+27\\
\text{let's group the "x" first}\\
(x^2-10x)+27\\
\text{let's make them a perfect square trinomial}\\
(x^2-10x+\square?)+27
$$
so, what number do you think we need there for a perfect square trinomial?
that is what number there multiplied by 2 will give me "10", the middle term

Answer 9

$$\bf ((x^2-10x)+27\\
(x^2-2(\square?x)+\square?^2)+27\\
$$

Answer 10

so, we just need that one number