Question

Help..

Answer 1

Solve by completing the square.

x^2+11x-9=0

Answer 2

@Nnesha

Answer 3

we can write this:
\[\Large {x^2} + 11x - 9 = {x^2} + 11x + \frac{{121}}{4} - \frac{{121}}{4} - 9\]

Answer 4

Um where did you get 121 and 4 from???

Answer 5

since we have this:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2} = {x^2} + 11x + \frac{{121}}{4}\]

Answer 6

Um okay.. Can you start at the beginning on how to solve this?

Answer 7

ok!

Answer 8

I rewrite the left side of your equation, adding and subtracting the same quantity, namely 121/4, so I get this equation:
\[\Large {x^2} + 11x + \frac{{121}}{4} - \frac{{121}}{4} - 9 = 0\]

Answer 9

then, I use this identity:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2} = {x^2} + 11x + \frac{{121}}{4}\]

Answer 10

so I can rewrite your starting equation, as below:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2} - \frac{{121}}{4} - 9 = 0\]

Answer 11

next, I nothe that:
\[ \Large - \frac{{121}}{4} - 9 = - \frac{{157}}{4}\]

Answer 12

after a substitution, I get this:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2} - \frac{{157}}{4} = 0\]

Answer 13

or:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2} = \frac{{157}}{4}\]

Answer 14

Uh?

Im here-

x^2+11x-9=0
(x+11/2)^2 -9=0
x^2+ 121/4 -9=0

I dont understand past that

Answer 15

Ive been using this method or factoring

https://www.youtube.com/watch?v=bclm1tJB-3g

Answer 16

In order to get an equivalent equation, I have to add and contemporarily I have to subtract 121/4, namely the same quantity

Answer 17

Um okay

Answer 18

so I get this equation:
\[\Large {x^2} + 11x + \frac{{121}}{4} - \frac{{121}}{4} - 9 = 0\]

Answer 19

the first three terms at the left side are the square of the subsequent binomial:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2}\]

Answer 20

Okay..

Answer 21

so, substituting, I can write this:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2} - \frac{{121}}{4} - 9 = 0\]

Answer 22

Okay

Answer 23

next I do this computation:
\[\Large - \frac{{121}}{4} - 9 = - \frac{{157}}{4}\]

Answer 24

and, again I substitute:
\[\Large {\left( {x + \frac{{11}}{2}} \right)^2} - \frac{{157}}{4} = 0\]

Answer 25

What? I seriously do not understand. How in the world do you get 157? I understand that (x+ 11/2)^2 equals x^2 +121/4 .. I assume the 11 over 2 is 11x divided by 2 which cant happen so it stays as a fraction. You said something about subtracting 121/4 and I assumed you meant to the other side of the equal sign but wasn't entirely sure. Im really trying to follow what your saying and I'm good in math but all this makes absolutely no sense so far.

Answer 26

Im still where I was earlier.

Answer 27

here is more details of my computation: