Question

When solving x2 + 6x = 10 by the completing the square method, what value is added to both sides?

9
5
4
3

Answer 1

You have to make it look like :

\(a^2 + b^2 + 2ab\) so that it can form into \((a+b)^2\)..

Answer 2

You have \(x^2\) term, that's nice.. You have also one \(6x\) term , that's more nice..

Answer 3

i still don't understand

Answer 4

I haven't started making you understand this yet.. :P

Answer 5

See, look it here can I write your expression as:

\[(x)^2 + 2 \cdot x \cdot (3) = 10\] Right?/

Answer 6

i guesssss

Answer 7

Please make sure your guess is a sure thing...

Answer 8

yeah you can but whats the point of doing that -_-

Answer 9

I am making it look like the way you can understand easily.. :P

Answer 10

ok

Answer 11

So, now can you compare it with :

\[(a)^2 + 2 \cdot a \cdot b \]
\[\color{green}{(x)^2 + 2 \cdot x \cdot 3 }\]

Compare these two expressions and tell me what is here a and b values??

Answer 12

b=3

Answer 13

a = 1?

Answer 14

Look for a more carefully... b=3 is superbly correct..

Answer 15

a = x

Answer 16

Mind blowing.. :P

Answer 17

Good, a = x here and b = 3, Okay??

Now, see do you know this formula : \(a^2 + 2ab + b^2 = (a+b)^2\)

Answer 18

no :(

Answer 19

Wait.. Do you know how to multiply??

Answer 20

yes... i've never seen that formula

Answer 21

If yes then multiply them:

\[(a+b) \times (a+b)\]

Answer 22

Use FOIL or any other technique you know..

Answer 23

(x+3)(x+3)
x^2 + 3x + 3x + 9
x^2 + 6x + 9

Answer 24

Oh wow, you made my work more easier..

See, in your question : you have \(x^2 + 6x\) but you have 9, right??

Answer 25

*I mean you don't have 9, right??

Answer 26

yeah so the answer is A?

Answer 27

Wait, answer is not important, I want you to know it more..

Answer 28

Now you make it complete square, you will add 9 both the sides:

\(x^2 + 6x + 9 = 10 + 9\)

Now itself you have calculated that \(x^2 + 6x + 9 = (x+30)^2\)

So, \((x+3)^2 = 19\)

Answer 29

That's not 30, but 3 there..

Answer 30

ohh so its right though?

Answer 31

I said, your answer is right, but do not incline yourself more towards answer, know the method or technique how to solve it, you can then get any answer of any question you face.. :)

Answer 32

ok thank you!

Answer 33

And Good, you co-operated very well.. :)

Answer 34

Welcome dear..

Answer 35

a way that is 10x easier is to take the b value and divide it by 2 and then square it

Answer 36

I want to tell that only, but you kept me away from that path.. :P

Answer 37

Here I wrote : \(2 \cdot x \cdot 3\) See, here I have separated 2 from 6 which is nothing but dividing 6 by 2, and you yourself replied, what for you are writing this? :(