Question

Solve a Quadratic useing comeplete the Square method

This problem makes no sense to me
The original problem is
X^2-6x=9

I know how to do these normally but there are a few that are odd

First we X^2 -6x +9=18

Then we factor

(x-3)^2 = 18

Which is (x-3) +- The Square root 18

i dont get how to finsih the problem when the end constant is not a perfect sqaure.
If you saw its (x-3) = 2* sqrt 3
Then what do you do?

My calculator says the answer is
x= -3*(SQRT2-1 or x= 3*SQRT2+1

Can someone explain the final step

Answer 1

look at it from a logical point of view; something sqaured = 18; it has to be either positive sqrt(18) or negative sqrt(18)

Answer 2

but then you have that -3 in the way, so get rid of it with a +3

Answer 3

Also i was hoping someone could help me to understand how to put these in my graphing calculaotr, i just got the thing and not sure how to put this stype of equation in
If you just enter the whole equation in y1 it doesnt grapgh anything,
If you type the first half in y1 and the =8 in y2 you get a grapgh but the interesects do not equal the answer

Answer 4

(-3 + x )^2 = 18

(-3 + (3+- sqrt(18)))^2 = 18

Answer 5

if its a ti 83 or such; hit y=; type in the equation using the "n,x,\(\theta\),..." key for the variable, and hit "graph"

Answer 6

its a ti 89 and i did that and it brings up the grapgh but doesnt draw anything

Answer 7

but back to the problem at hand lol i dont follow what your saying, i know that (x-3)^2=18 means that (x-3)=+ or minus The SQRT of 18 but sense 18 is not a perfect sq you the 2 Sqrt 3 I still dont get what to do next

Answer 8

\(x-3 = \pm\sqrt{18}\); add 3 to each side
+3 +3
--------------------
\(x =3 \pm\sqrt{18}\)

Answer 9

18 = 9*2

sqrt(9*2) = sqrt(9) * sqrt(2) = 3 sqrt(2)

Answer 10

you get 2 answers that work;

\[x = 3+3\sqrt{2}\]or
\[x = 3-3\sqrt{2}\]

Answer 11

wait one second i was staqrting to follow u

Answer 12

i get what you are saying about (x-3)= SQRT 18 now add +3 to both sides right
but wouldnt that give you x= -2 SQRT 3 +3 and x= 2 SQRT3 +3 I dont get were the minus comes from

Answer 13

lets go back to the basics of what happens when we square something ...

Answer 14

x^2 = 4 ; what are our options for x?

Answer 15

(-2)^2 = 4 AND (+2)^2 = 4