Question

Solve x2 - 7x = -13.

Answer 1

do you know how to solve quadratic equations ?
tried this one ?

Answer 2

yea but i need to use the completing the square formula to solve it.

Answer 3

so, you know that method ?
basically you make left side a perfect square by adding/subtracting something and then take square root.

Answer 4

so, firstly, can you tell me what is the co-efficient of 'x' in your equation ?

Answer 5

yea i know the method but it confusesme when i try to use it

Answer 6

idk man like i said whei try to use that methodit confuses me and i draw a blank on how to solve it

Answer 7

i will tell you step by step , how to solve it, ok ? :)
so, step 1.
divide the co-efficient of 'x' by 2

so, do you know what is the co-efficient of 'x' in your equation x2 - 7x = -13 ?

Answer 8

ok so i divide just x or both of the x's by 2

Answer 9

if i divide just x by 2 i get x

Answer 10

so, the co-efficient of 'x' means the constant that is multiplied to 'x'
like in x^2+12x , the co-efficient is 12
so, whats the co-efficient in x2 - 7x = -13 ?

Answer 11

7 is the c=efficiant so if i divide it by 2 i get 7/2

Answer 12

correct!
step 2 :
square it!
(7/2)^2 = ... ?

Answer 13

when i square it i get 14/4

Answer 14

7^2 = 7*7 = ... ?

Answer 15

oh it would be 49/4

Answer 16

yes!

Answer 17

step 3 :
now add 49/4 on both sides

Answer 18

so it would be \[x ^{2}-7x+\frac{ 49 }{ 4}=-13+\frac{ 49 }{ 4 }\]

Answer 19

correct!
now notice that left side is a perfect square of ... ?
can you figure out ?

Answer 20

it a perfect square of 7

Answer 21

left side is perfect square of x -7/2
isn't it ?

Answer 22

yea it is

Answer 23

now what would i do

Answer 24

simplify the right side
and just take square root on both sides

Answer 25

ok if i square the right i get\[\frac{ 7 }{ 2 }+\sqrt{-13}\]

Answer 26

no, no....first simplify the right side! before taking square root

Answer 27

-13 + 49/4 = ... ?

Answer 28

36/4

Answer 29

no.... how you got 36 ?

Answer 30

i subtracted 13 from 49

Answer 31

thats not the way to subtract fractions
-13 + 49/4 = (-13*4+ 49)/4 = ... ?

Answer 32

ok i got -3 for the top number so it would -3/4?

Answer 33

yes!

Answer 34

yaaaaay :-P

Answer 35

now you can take square root on both sides

Answer 36

ok how would i square -3/4

Answer 37

not square, square root

Answer 38

tht what i meant .how would i sqaure root it

Answer 39

you know about imaginary number 'i' ?

Answer 40

yea i do.

Answer 41

so it would be\[i \sqrt{\frac{ -3 }{ 4 }}\]?

Answer 42

once 'i' is outside, the negative sign won't be inside still, right ?
\(\large \sqrt{\frac{ -3 }{ 4 }}=\sqrt {-1} \sqrt{\frac{ 3 }{ 4 }}=i \sqrt{\frac{ 3 }{ 4 }} = i\frac{\sqrt 3}{2}\)
got this ?

Answer 43

yea got it.

Answer 44

n would i multiply the 3 by 2?

Answer 45

wait, whats on the left side after you take square root ?

Answer 46

\[\left( x-7 \right)^{2}\]

Answer 47

its (x-7/2)^2 !

Answer 48

oh ok

Answer 49

so, after taking square root on both sides
we get
\(\large x-7/2 = \pm i \sqrt 3/2\)

got this ?
just add 7/2 on both sides to get 2 values of 'x' !

Answer 50

ok so it would be\[x=\sqrt{\frac{ 10 }{ 2}}\]?

Answer 51

no, you cannot add a real number with an imaginary number..

Answer 52

its just
\(\large x = (1/2)(7\pm i\sqrt 3)\)

Answer 53

cannot simplify further, so final answer :)
got this ? any doubts anywhere ?

Answer 54

ooooohhhh ok i get it now!:) thanks man!

Answer 55

welcome ^_^