Question

Completing the Square: x^2+8x-9=0

Answer 1

(x+4)^2, expand it.

Answer 2

well theres a logical approach to such questions..
but i'll tell you 1 shortcut..
in ax^2 + bx +c ,, replace x by (y - b/2a)
after simplifying,,replace back value of x..

Answer 3

x^2+8x+16

Answer 4

Now, how do you make that to be the same as what you started with?

Answer 5

U understand me? What do you have to do to the expanded equation to get back to the first equation?

Answer 6

im not sure what I have to do...I am very challenged here.

Answer 7

Just subtract 25, right?

Answer 8

how did you get that?

Answer 9

16 and 9

Answer 10

^2+8x+16
x^2+8x-9

Difference 25

Answer 11

ok

Answer 12

So if we take (x+4)^2 and subtract 25 from it we are back to where we started.

Answer 13

(x+4)^2 -25 = 0 or

(x-4)^2 = 25 whci is called completing the square.

Answer 14

The only tricky bit is coming upo with (x+4)^2 for which
you just take half of the number of x's

Answer 15

couldn't we only do that here because they were perfect squares?

Answer 16

In theory you can complete the square with any quadratic.
In fact, that is how the quadratic formula is derived.

Answer 17

can we look at another one?

Answer 18

x^2 + 10x +6 = 0

Answer 19

so expand x^2+5

Answer 20

Correct (after you have done a few, you will be able to do it in your head)

Answer 21

x^2+10x+25

Answer 22

(x+5)^2

Answer 23

yeah, I can't do it my head...

Answer 24

So the difference is?

Answer 25

19

Answer 26

So complete the square...

Answer 27

x^2+10x+19=0

Answer 28

Nope.

Answer 29

or its what the x = x =19

Answer 30

(x+5)^2 -19 = 0

Answer 31

what about when the number are not even such as x2-6x+17=0

Answer 32

(x-3)^2 + 8= 0

Answer 33

so starting with expanding...x^2+9x+9

Answer 34

All you are doing is rewriting the original equation as the sum of a square and a constant.

Answer 35

x^2-6x+9

Answer 36

yes I messed that one up

Answer 37

Last one, x^2+ 9x -40 =0

Answer 38

my teacher put the -8 on a square root? W an answer of x=3+- i square root 8...??

Answer 39

sqrt(ab) = sqrt(a)*sqrt(b) so
Sqrt -8 = Sqrt(-1)*Sqrt(8) = i*8 (or 8i)

Answer 40

are these just logistics of how to write the answer?

Answer 41

I wrote that last wrong
sqrt(ab) = sqrt(a)*sqrt(b) so
Sqrt -8 = Sqrt(-1)*Sqrt(8) = i*sqrt8 (or sqrt(8)i)

Logistics?

Answer 42

ok so you would write it 3 +- i sq rt 8 ?

Answer 43

That's OK but usually you reduce the sqrt 8 to 2sqrt2

Answer 44

Teacher will probably dock you a mark if you don't reduce it.

Answer 45

ok so the last example you gave...not sure what to do now if the number isn't even...

Answer 46

Exactly the same as before, just take the half of it

Answer 47

(x +9/2)^2

Answer 48

And if it was x^2 + bx +c you still do it just the same
(x+b/2)^2

Answer 49

Anyway, I leave you to practice...:-)

Answer 50

thank you very much!