Janu16
  • Janu16
Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 10x + ___?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Janu16
  • Janu16
@SolomonZelman
SolomonZelman
  • SolomonZelman
Ok
Janu16
  • Janu16
so how do you figure out the third number

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SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) do you understand this rule?
Janu16
  • Janu16
yaa but is there a name for this stuff
Janu16
  • Janu16
i actually take online class and they haven't teached the rules you are teaching me
SolomonZelman
  • SolomonZelman
Oh, then you are a little bit behind, I guess.
SolomonZelman
  • SolomonZelman
I don't recall its name in particular, but I don't think that matters that much,.
Janu16
  • Janu16
they have teached me y=a(x-h)^2+h and ax^2+bx+c for this lessom
Janu16
  • Janu16
y=a(x-h)^2+k
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2= }\) \(\large\color{black}{ \displaystyle (x+\color{red}{ a})(x+\color{red}{ a})= }\) \(\large\color{black}{ \displaystyle x\cdot x+x\cdot\color{red}{ a}+x\cdot \color{red}{ a}+\color{red}{ a}\cdot\color{red}{ a}= }\) \(\large\color{black}{ \displaystyle x^2+x\color{red}{ a}+x \color{red}{ a}+\color{red}{ a}^2= }\) \(\large\color{black}{ \displaystyle x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) `--------------------------------------------` Is this process I did familiar to you?
Janu16
  • Janu16
yaas
Janu16
  • Janu16
this is what i learned
SolomonZelman
  • SolomonZelman
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?
Janu16
  • Janu16
mhm
SolomonZelman
  • SolomonZelman
and we want to get \(x^2+10x\) peace of the equation, to be a perfect square.
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle x^2+10x+{?} }\)
SolomonZelman
  • SolomonZelman
(you want to get your equation to be like: \(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) )
SolomonZelman
  • SolomonZelman
10 is same as 2a, right?
Janu16
  • Janu16
ook
SolomonZelman
  • SolomonZelman
Compere these two: \(\large\color{black}{ \displaystyle x^2+10x+{?} }\) \(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)
SolomonZelman
  • SolomonZelman
Compare*
SolomonZelman
  • SolomonZelman
((the question mark is \(a^2\) ))
SolomonZelman
  • SolomonZelman
so if 10 is 2a, then \(a^2\) is going to be equal to what?
Janu16
  • Janu16
soory hold on im lagging
Janu16
  • Janu16
2ax? or a2
SolomonZelman
  • SolomonZelman
Again, 2a in our case is what?
Janu16
  • Janu16
10
SolomonZelman
  • SolomonZelman
so if 2a=10 then a\(^2\)=?
Janu16
  • Janu16
10?
SolomonZelman
  • SolomonZelman
ok, 2a=10 then a=?
Janu16
  • Janu16
im really not sure about thiss
SolomonZelman
  • SolomonZelman
2a=10 divide by 2 on both sides, and you get that a=5
Janu16
  • Janu16
wait oyu divide?
SolomonZelman
  • SolomonZelman
Yes, if 2 times a is 10. Then one a is 5.
Janu16
  • Janu16
ohhok so divide so the last blank would be 5
SolomonZelman
  • SolomonZelman
(( 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 \(25\).
Janu16
  • Janu16
5^2? right
SolomonZelman
  • SolomonZelman
yes, and that is same thing as "5×5". And this is going to be equal to 25 as you know.
SolomonZelman
  • SolomonZelman
So, now you have: \(\large\color{black}{ \displaystyle x^2+10x+{\underline{25}} }\) \(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)
Janu16
  • Janu16
ohok and what was tht formula you used? I just wanna write it down
SolomonZelman
  • SolomonZelman
\(\LARGE\color{black}{ \displaystyle \color{blue}{x}^2+2\color{red}{a}\color{blue}{x}+\color{red}{a}^2=(\color{blue}{x}+\color{red}{a})^2 }\)

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