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

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

Mathematics
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Ok
so how do you figure out the third number

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\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) do you understand this rule?
yaa but is there a name for this stuff
i actually take online class and they haven't teached the rules you are teaching me
Oh, then you are a little bit behind, I guess.
I don't recall its name in particular, but I don't think that matters that much,.
they have teached me y=a(x-h)^2+h and ax^2+bx+c for this lessom
y=a(x-h)^2+k
\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2= }\) \(\large\color{black}{ \displaystyle (x+\color{red}{ a})(x+\color{red}{ a})= }\) \(\large\color{black}{ \displaystyle x\cdot x+x\cdot\color{red}{ a}+x\cdot \color{red}{ a}+\color{red}{ a}\cdot\color{red}{ a}= }\) \(\large\color{black}{ \displaystyle x^2+x\color{red}{ a}+x \color{red}{ a}+\color{red}{ a}^2= }\) \(\large\color{black}{ \displaystyle x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) `--------------------------------------------` Is this process I did familiar to you?
yaas
this is what i learned
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?
mhm
and we want to get \(x^2+10x\) peace of the equation, to be a perfect square.
\(\large\color{black}{ \displaystyle x^2+10x+{?} }\)
(you want to get your equation to be like: \(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) )
10 is same as 2a, right?
ook
Compere these two: \(\large\color{black}{ \displaystyle x^2+10x+{?} }\) \(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)
Compare*
((the question mark is \(a^2\) ))
so if 10 is 2a, then \(a^2\) is going to be equal to what?
soory hold on im lagging
2ax? or a2
Again, 2a in our case is what?
10
so if 2a=10 then a\(^2\)=?
10?
ok, 2a=10 then a=?
im really not sure about thiss
2a=10 divide by 2 on both sides, and you get that a=5
wait oyu divide?
Yes, if 2 times a is 10. Then one a is 5.
ohhok so divide so the last blank would be 5
(( 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 \(25\).
5^2? right
yes, and that is same thing as "5×5". And this is going to be equal to 25 as you know.
So, now you have: \(\large\color{black}{ \displaystyle x^2+10x+{\underline{25}} }\) \(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)
ohok and what was tht formula you used? I just wanna write it down
\(\LARGE\color{black}{ \displaystyle \color{blue}{x}^2+2\color{red}{a}\color{blue}{x}+\color{red}{a}^2=(\color{blue}{x}+\color{red}{a})^2 }\)

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