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

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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)   (Show Source): You can put this solution on YOUR website!




Isolate the variable terms by
adding 33 to both sides:



[If there were a coefficient for  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 .


Now square .  

Add  to both sides of the equation 



Combine the right side: 



Factor the left side:



Write the left side as the square of
a binomial:



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



=±



Using the +



Using the -



The solutions are  and 

Edwin
Answer by lwsshak3(11628)   (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
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