## Janu16 one year ago Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 10x + ___?

1. Janu16

@SolomonZelman

2. SolomonZelman

Ok

3. Janu16

so how do you figure out the third number

4. 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?

5. Janu16

yaa but is there a name for this stuff

6. Janu16

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

7. SolomonZelman

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

8. SolomonZelman

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

9. Janu16

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

10. Janu16

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

11. 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?

12. Janu16

yaas

13. Janu16

this is what i learned

14. 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?

15. Janu16

mhm

16. SolomonZelman

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

17. SolomonZelman

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

18. SolomonZelman

(you want to get your equation to be like: $$\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }$$ )

19. SolomonZelman

10 is same as 2a, right?

20. Janu16

ook

21. SolomonZelman

Compere these two: $$\large\color{black}{ \displaystyle x^2+10x+{?} }$$ $$\large\color{blue}{ \displaystyle x^2+2ax+a^2 }$$

22. SolomonZelman

Compare*

23. SolomonZelman

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

24. SolomonZelman

so if 10 is 2a, then $$a^2$$ is going to be equal to what?

25. Janu16

soory hold on im lagging

26. Janu16

2ax? or a2

27. SolomonZelman

Again, 2a in our case is what?

28. Janu16

10

29. SolomonZelman

so if 2a=10 then a$$^2$$=?

30. Janu16

10?

31. SolomonZelman

ok, 2a=10 then a=?

32. Janu16

33. SolomonZelman

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

34. Janu16

wait oyu divide?

35. SolomonZelman

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

36. Janu16

ohhok so divide so the last blank would be 5

37. 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 $$25$$.

38. Janu16

5^2? right

39. SolomonZelman

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

40. SolomonZelman

So, now you have: $$\large\color{black}{ \displaystyle x^2+10x+{\underline{25}} }$$ $$\large\color{blue}{ \displaystyle x^2+2ax+a^2 }$$

41. Janu16

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

42. SolomonZelman

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