SOLUTION: Solving equations by completing the square! r^2+2r-33=0. 6. a^2-2a-48=0. thank you!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solving equations by completing the square! r^2+2r-33=0. 6. a^2-2a-48=0. thank you!      Log On


   

Question 886476: Solving equations by completing the square!
r^2+2r-33=0. 6. a^2-2a-48=0. thank you!
Found 2 solutions by Edwin McCravy, lwsshak3:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


r%5E2%2B2r-33=0

Isolate the variable terms by
adding 33 to both sides:

r%5E2%2B2r=33

[If there were a coefficient for r%5E2 other than 1, you
would divide thru by that coefficient.  But since the coefficient
is 1, this is not necessary, but it might be in some problems.]

To the side, multiply the coefficient of r by 1%2F2.
%282%29%2A%281%2F2%29=1

Now square 1.  1%5E2=1

Add 1 to both sides of the equation r%5E2%2B2r=33

r%5E2%2B2r%2B1=33%2B1

Combine the right side: 33%2B1

r%5E2%2B2r%2B1=34

Factor the left side:

%28r%2B1%29%28r%2B1%29=34

Write the left side as the square of
a binomial:

%28r%2B1%29%5E2=34

Take the square root of both sides,
remembering the ± on the right:

sqrt%28%28r%2B1%29%5E2%29+=+%22%22+%2B-+sqrt%2834%29

r%2B1=±sqrt%2834%29

x=-1+%2B-+sqrt%2834%29

Using the +

x=-1+%2B+sqrt%2834%29

Using the -

x=-1+-+sqrt%2834%29

The solutions are -1%2Bsqrt%2834%29 and -1-sqrt%2834%29

Edwin

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solving equations by completing the square!
r^2+2r-33=0. 6. a^2-2a-48=0.
***
r^2+2r-33=0
add 1/2 the coefficient of the r-term squared, then add (-1) to balance the equation.
(r^2+2r+1)-1-33=0
(x+1)^2=34
take sqrt of both sides
x+1=±√34
x=-1±√34
x=-1-√34
or
x=-1+√34
..
a^2-2a-48=0
add 1/2 the coefficient of the a-term squared, then add (-1) to balance the equation.
(a^2-2a+1)-1-48=0
(x-1)^2=49
take sqrt of both sides
x-1=±√49
x=1±7
x=-6
or
x=8