SOLUTION: I really need help with these last three problems and then I am done with the course! PLEASE HELP I am really confused.... (Solve by completing the square.) 1.x^2-6x=1 2.2x^2-

Algebra ->  Test  -> Lessons -> SOLUTION: I really need help with these last three problems and then I am done with the course! PLEASE HELP I am really confused.... (Solve by completing the square.) 1.x^2-6x=1 2.2x^2-      Log On


   

Question 317970: I really need help with these last three problems and then I am done with the course! PLEASE HELP I am really confused....
(Solve by completing the square.)
1.x^2-6x=1
2.2x^2-3x+1=x0
3.x^2-x-1=0
Thank you for your time and help.
Found 3 solutions by stanbon, josmiceli, checkley77:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(Solve by completing the square.)
1.x^2-6x=1
x^2-6x+9 = 1+9
(x-3)^2 = 10
x-3 = sqrt(10) or x-3 = -sqrt(10)
x = 3+sqrt(10) or x = 3-sqrt(10)
--------------------------------------------------
2. 2x^2-3x+1= 0
2x^2 - 3x = -1
2(x^2-(3/2)x) = -1
2(x^2-(3/2)x+(3/4)^2) = -1 + 2(3/4)^2
2(x-(3/2))^2 = 1/8
(x-(3/2))^2 = 1/16
x-(3/2) = +-1/4
x = (3/2)+(1/4) or x = (3/2)-(1/4)
x = (7/4) or x = 5/4
---------------------------------------------------
3.x^2-x-1=0
I'll leave this one to you.
Cheers,
Stan H.
==============

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Completing the square can be expressed in one sentence:
"Take 1/2 of the coefficient of x, square it, then add it to both
sides." The only other thing is to get the constant term on
the right side.
(1) x%5E2+-+6x+=+1
x%5E2+-+6x+%2B+%28-6%2F2%29%5E2++=+1+%2B+%28-6%2F2%29%5E2
x%5E2+-+6x+%2B+9+=+1+%2B+9
%28x+-+3%29%5E2+=+10
Take the square root of both sides
x+-+3+=+0+%2B-sqrt%2810%29
x+=+3+%2B-sqrt%2810%29 (note there are 2 answers)
(2)?
(3) x%5E2+-+x+-+1+=+0
x%5E2+-+x+%2B+%28-1%2F2%29%5E2+=+1+%2B+%28-1%2F2%29%5E2
x%5E2+-+x+%2B+1%2F4+=+1+%2B+1%2F4
%28x+-+1%2F2%29%5E2+=+5%2F4
x+-+1%2F2+=0+%2B-+sqrt%285%29%2F2
x+=+1%2F2+%2B-+sqrt%285%29%2F2
You can check answers by plugging them back into original equation


Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
1.x^2-6x=1 add 9 to both sides.
x^2-6x+9=1+9
(x-3)^2=10 take the sqrt of both sides.
x-3=sqrt10
x-3=3.1623
x=3.1623+3
x=6.1623 ans.
Proof:
6.1623^2-6*6.1623=1
37.97-36.07=1
1=1
------------------------
2.2x^2-3x+1=0
2.2x^2-3x+1.022 =-1+1.022
(1.4832396x-1.0113)^2=.022
1.4832396x-1.0113=sqrt.022
1.4832396x-1.0113=.148324
1.4832396x=.148324+1.011
1.4832396x=1.159324
x=1.159324/1.4832396
x=.78 ans
Proof:
2.2*78^2-3*.78+1=0
2.2*.6084-2.34+1=0
1.338-2.34+1=0
2.338~2.34
3.x^2-x-1=0
-------------------------
3.x^2-x-1=0
x^2-x+.25=1+.25
(x-.5)^2=1.25
x-.5=sqrt1.25
x-.5=1.118
x=1.118+.5
x=1.618ans.
Proof:
1.618^2-1.618-1=0
2.618-1.618-1=0
2.618-2.618=0
0=0