Question

find the solution to the quadratic equation by completing the square
x^2+6x=7 @siegel

Answer 1

well first get the squared part alone, so how do you do that?

Answer 2

um subract 6x from both sides?

Answer 3

right so what is your equation now?

Answer 4

x^2=7-6x

Answer 5

\[x^{2} + 6x - 7 = 0\]
\[(x^{2}+6x-9+9) - 7 = 0\]
\[(x+3)^{2}-9-7 = 0\]
\[(x+3)^{2}-16 = 0\]
Therefore x = -3 and y = -16
(-3,-16) is the solution!

Answer 6

wait I did something wrong, the other person got it, would you like me to walk you through it?

Answer 7

yeah because i still dont understand it...

Answer 8

Okay, sorry about my slip up.
keep the equation the same but think about FOIL.
we are focusing on the left side, you have an a value and a b value, how would you make it a quadratic equation?

Answer 9

the equation would have to =0? so then i guess you would have to subtract 7 from both sides.

Answer 10

not exactly, remember we are only dealing with the left side, how would you make\[X ^{2}+6X\] into a perfect square trinomial, you can add anything.
wait do you know about perfect square trinomeals?

Answer 11

9?

Answer 12

right, so how did you get that?

Answer 13

well if you factored it using FOIL and knowing it was a perfect square the last term would have to be a perfect square...and the only number that adds up to 6 being a perfect square is 3. if that makes any sence

Answer 14

No you are totaly on track. a quicker way is to divide the b cooeficient by 2 then square it. now what does your equation look like?

Answer 15

\[x ^{2}+6x+9=7\]

Answer 16

close but remember what you do to one side you have to do to the other

Answer 17

so wait then you would multiply it by 3? making it 21?

Answer 18

no you added 9 to one side to make it a pst, so wouldn't you add 9 to the other side?

Answer 19

oh! now i understand! so then the equation would be x^2+6x+9=16

Answer 20

right! Okay, so remember how you had that 3, well what is the factor of x^2+6x+9

Answer 21

ok..

Answer 22

factors sorry.

Answer 23

okay so then what do you do?

Answer 24

well does the equation look like now?

Answer 25

x^2+6x+9=16

Answer 26

now factor the left side

Answer 27

I promise this will all make sense.

Answer 28

(x+3)^2

Answer 29

=16

Answer 30

so plug that into the equation

Answer 31

into the quadratic equation?

Answer 32

well if (X+3)^2=16
how could we get rid of the ^2?

Answer 33

by.....taking the square root from both sides?

Answer 34

right! so what do we have now?

Answer 35

x+3=4

Answer 36

yes the only thing is, what do you do when you take the square root of a number,
(this will give you the two answers)

Answer 37

you have a positive and a negative answer

Answer 38

yes so what is the equation?

Answer 39

well you would have the same equation but when you solve it you would end up with 1 and negative 7

Answer 40

shoot class is over. I'll be back though if you are still on. thanks :)

Answer 41

YES! after taking the square root of both sides you have\[(X+3)=\pm4\]
+4-3=1 and -4-3=-7. You are awesome! great job

Answer 42

awesome!!! thanks :)

Answer 43

No problem any time!

Answer 44

okay same concept but different equations. can you help? x^2+12x=-11

Answer 45

ok so how do you make the left side a pst

Answer 46

6?

Answer 47

oh wait I think i figured it out...the answer would be x=-1 and-11?

Answer 48

what about the ones like this? x^2+2x-4=0?

Answer 49

wait the last one how do you get -1 and -11, I think you have to switch the signs.
for the next one how do you make the left side a binomial?

Answer 50

subtract 4 from both sides?

Answer 51

close it's a negative 4 so how do you eliminate it?

Answer 52

you would subtract -4 from both sides so your equation would be...x^2+2x=-4

Answer 53

I see what you're thinking but you're subtracting -4 from both sides, what do you do when you subtract a negative?

Answer 54

im not sure...switch the sign?

Answer 55

5-(-7) = 5+7

Answer 56

oh they cancel!

Answer 57

yep so what does the equation look like now?

Answer 58

x^2+2x=4

Answer 59

right! so what comes next?

Answer 60

you would have to turn it into a perfect square. so the equation would be..x^2+2x+4=8

Answer 61

close, what do you do to the b value?

Answer 62

wait you dont do anything to B.

Answer 63

go back to the binomial. x^2+2x=4
divide the b value by 2 and then square it.

Answer 64

that would be 1

Answer 65

right so what is the equation

Answer 66

x^2+x+4=8?

Answer 67

no...remember the number you get has to make a pst. 1 will end up being the c value. try factering it with 1 as the a value, 2 as the b value and 1 as the c value.

Answer 68

hahaha wait im totally confused.

Answer 69

ok, so in this problem the answer will not be perfect, but go with it.
start from the beginning, you add 4 to both sides
x^2+2x=4
now how do you make (x^2+2x) a perfect square trinomial

Answer 70

by adding 4 to both sides

Answer 71

no, although I agree, that is the logical first choice. but remember, the c value times 2 has to be equal to the b value

Answer 72

so if it has to be the same then wouldnt it be 2?

Answer 73

b is always twice the square root of c
so
c is ^2 of half of b

Answer 74

hmm......that would be 1

Answer 75

yes, this is a bad example but yes.
so write out the equation

Answer 76

x^2+2x+1=4

Answer 77

check the right side

Answer 78

=5

Answer 79

right, so what's next?

Answer 80

put in quadratic?

Answer 81

well factor the left side

Answer 82

oh so then it would be x+1)=5

Answer 83

Squared

Answer 84

like (x+1)^2=5

Answer 85

great
what do you do next

Answer 86

take the square root from both sides

Answer 87

so what happens to the right side
PS keep it in radical form.

Answer 88

it would be x+1=positive and negative \[\sqrt{5}\]

Answer 89

sorry if im like bugging you but I have two more problems that are the same type that Im not sure about... 2x^2+3x-5=0 I cant make this a perfect square

Answer 90

No problem
also with x^2+12x=-11 I think you need to switch your signs for your answer.
ok this is something that gets easier with practice. what do you think you do first

Answer 91

you have to get the parts with the x alone. so you would add 5 to both sides making the equation 2x^2+3x=5

Answer 92

actually for this one the first thing you do is get the cooeficient of 2x^2 to 1.
how do you think you do that?
technically you can move the five first just remember to do the same thing to both sides.

Answer 93

what do you mean get it to 1?

Answer 94

you are going to divide everything by 2. I know this is weird but it's easier with even numbers.

Answer 95

but that seems weird because then you have x^2+3x

Answer 96

well you divide EVERYTHING by 2 so 3 becomes 3/2 or 1.5

Answer 97

so then you have x^2+1.5x=2.5?

Answer 98

exactly, here you're going to want a calculator. I don't know if your teacher want's it in decimal or fraction form so use your best judgement. What do you think you do next?