Question

Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 10x + ___?

Answer 1

@SolomonZelman

Answer 2

Ok

Answer 3

so how do you figure out the third number

Answer 4

\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\)

do you understand this rule?

Answer 5

yaa but is there a name for this stuff

Answer 6

i actually take online class and they haven't teached the rules you are teaching me

Answer 7

Oh, then you are a little bit behind, I guess.

Answer 8

I don't recall its name in particular, but I don't think that matters that much,.

Answer 9

they have teached me y=a(x-h)^2+h and ax^2+bx+c for this lessom

Answer 10

y=a(x-h)^2+k

Answer 11

\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2= }\)

\(\large\color{black}{ \displaystyle (x+\color{red}{ a})(x+\color{red}{ a})= }\)

\(\large\color{black}{ \displaystyle x\cdot x+x\cdot\color{red}{ a}+x\cdot \color{red}{ a}+\color{red}{ a}\cdot\color{red}{ a}= }\)

\(\large\color{black}{ \displaystyle x^2+x\color{red}{ a}+x \color{red}{ a}+\color{red}{ a}^2= }\)

\(\large\color{black}{ \displaystyle x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\)

`--------------------------------------------`
Is this process I did familiar to you?

Answer 12

yaas

Answer 13

this is what i learned

Answer 14

ok, so thus we know that:
\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\)

Okay?

Answer 15

mhm

Answer 16

and we want to get \(x^2+10x\) peace of the equation, to be a perfect square.

Answer 17

\(\large\color{black}{ \displaystyle x^2+10x+{?} }\)

Answer 18

(you want to get your equation to be like:

\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) )

Answer 19

10 is same as 2a, right?

Answer 20

ook

Answer 21

Compere these two:

\(\large\color{black}{ \displaystyle x^2+10x+{?} }\)
\(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)

Answer 22

Compare*

Answer 23

((the question mark is \(a^2\) ))

Answer 24

so if 10 is 2a, then \(a^2\) is going to be equal to what?

Answer 25

soory hold on im lagging

Answer 26

2ax? or a2

Answer 27

Again, 2a in our case is what?

Answer 28

10

Answer 29

so if
2a=10

then a\(^2\)=?

Answer 30

10?

Answer 31

ok, 2a=10
then a=?

Answer 32

im really not sure about thiss

Answer 33

2a=10
divide by 2 on both sides, and you get that
a=5

Answer 34

wait oyu divide?

Answer 35

Yes, if 2 times a is 10. Then one a is 5.

Answer 36

ohhok so divide so the last blank would be 5

Answer 37

(( a\(^2\) is same as \(a \times a\). ))
So, if a is 5, then \(a \times a\) is \(5\times 5\).
That will be equal to \(25\).

Answer 38

5^2? right

Answer 39

yes, and that is same thing as "5×5".
And this is going to be equal to 25 as you know.

Answer 40

So, now you have:

\(\large\color{black}{ \displaystyle x^2+10x+{\underline{25}} }\)

\(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)

Answer 41

ohok and what was tht formula you used? I just wanna write it down

Answer 42

\(\LARGE\color{black}{ \displaystyle \color{blue}{x}^2+2\color{red}{a}\color{blue}{x}+\color{red}{a}^2=(\color{blue}{x}+\color{red}{a})^2 }\)