SOLUTION: Completing the square. 1.)x^2+6x=7 2.) x^2+8x=9 3.) 9x^2+19x=-8 (solve by completing the square an coefficient of x^2 is 1) I'm looking for the processes of these. The

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Completing the square. 1.)x^2+6x=7 2.) x^2+8x=9 3.) 9x^2+19x=-8 (solve by completing the square an coefficient of x^2 is 1) I'm looking for the processes of these. The       Log On


   



Question 1026796: Completing the square.
1.)x^2+6x=7
2.) x^2+8x=9
3.) 9x^2+19x=-8 (solve by completing the square an coefficient of x^2 is 1)
I'm looking for the processes of these. The book examples don't help.

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
Completing the square.
1.)x^2+6x=7
2.) x^2+8x=9
3.) 9x^2+19x=-8 (solve by completing the square an coefficient of x^2 is 1)
I'm looking for the processes of these. The book examples don't help.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1) x%5E2%2B6x = 7,

   x%5E2+%2B+6x+-+7 = 0

   %28x%5E2+-+6x+%2B+9%29+-+9+-+7 = 0,      ( I added and distracted 9 )

   %28x-3%29%5E2+-+16 = 0              ( %28x%5E2+-+6x+%2B+9%29 = %28x-3%29%5E2 )

   %28x-3%29%5E2 = 16,                 ( Now take the square root from both sides )

   x-3 = +/- 4,

   x = 3 +/- 4,

   x = 7 and/or x = -1.


2)  x^2+8x=9      is exactly the same.  Do it yourself.

3)  9x^2+19x=-8   I suspect you missed something here.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Completing the square.
1.)x^2+6x=7
2.) x^2+8x=9
3.) 9x^2+19x=-8 (solve by completing the square an coefficient of x^2 is 1)
I'm looking for the processes of these. The book examples don't help.
x%5E2+%2B+6x+=+7
x%5E2+%2B+6x+%2B+%28%281%2F2%29b%29%5E2+=+7+%2B+%28%281%2F2%29+%2A+b%29%5E2 ------ Adding 1%2F2 the value of b, and then squaring the result
x%5E2+%2B+6x+%2B+%28%281%2F2%296%29%5E2+=+7+%2B+%28%281%2F2%29+%2A+6%29%5E2 ------ Adding 1%2F2 ------ Substituting + 6 for b
x%5E2+%2B+6x+%2B+3%5E2+=+7+%2B+3%5E2
%28x+%2B+3%29%5E2+=+7+%2B+9
%28x+%2B+3%29%5E2+=+16
sqrt%28%28x+%2B+3%29%5E2%29+=+%22+%22%2B-+sqrt%2816%29 ------- Taking square root of both sides
x+%2B+3+=+%22+%22%2B-+4
x+=+%22+%22%2B-+4+-+3
highlight_green%28matrix%281%2C+7%2C+x%2C+%22=%22%2C+1%2C+or%2C+x%2C+%22=%22%2C+-+7%29%29
Follow the above steps and you should be able to do number 2
Number 3 can get quite MESSY. Did you really mean: 9x%5E2+%2B+19x+=+-+8, or something else? If it's correct, factor
out 9 on both sides to get a coefficient of 1 on x%5E2, and once again, follow the steps in number 1