SOLUTION: My problem is to use the quadratic equation for: (r-3)(r+9)=16. I'm up to the step where r equals pus or minus the square root of 208 divide by 2. At this point I'm not sure how to

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: My problem is to use the quadratic equation for: (r-3)(r+9)=16. I'm up to the step where r equals pus or minus the square root of 208 divide by 2. At this point I'm not sure how to      Log On


   

Question 593408: My problem is to use the quadratic equation for: (r-3)(r+9)=16. I'm up to the step where r equals pus or minus the square root of 208 divide by 2. At this point I'm not sure how to factor out the next three steps to get the solution step. My answer came out to be {-3+2 square root over 2 , -3-2 square root over 2}
I did my best here to describe the symbols that I can't enter in this example. Thanks, James
Found 2 solutions by ankor@dixie-net.com, Earlsdon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
My problem is to use the quadratic equation for: (r-3)(r+9)=16.
FOIL
r^2 + 9r - 3r - 27 = 16
r^2 + 6x - 27 - 16 = 0
r^2 + 6x - 43 = 0
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=r, a=1, b=6, c=-43
r+=+%28-6+%2B-+sqrt%286%5E2-4%2A1%2A-43+%29%29%2F%282%2A1%29+
:
r+=+%28-6+%2B-+sqrt%2836+%2B+172%29%29%2F2+
:
r+=+%28-6+%2B-+sqrt%28208%29%29%2F2+
I think here you went astray somewhere
Factor inside the radical to reveal a perfect square
r+=+%28-6+%2B-+sqrt%2816%2A13%29%29%2F2+
Extract the square root of 16
r+=+%28-6+%2B-+4sqrt%2813%29%29%2F2+
Two solutions
r+=+%28-6+%2B+4sqrt%2813%29%29%2F2+
r+=+-3+%2B+2sqrt%2813%29%29+
and
r+=+-3+-+2sqrt%2813%29%29+


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
%28r-3%29%28r%2B9%29+=+16 Simplify.
r%5E2%2B6r-27+=+16 Subtract 16 from bothsides.
r%5E2%2B6r-43+=+0 Solve using the quadratic formula.
r+=+%28-6%2B-sqrt%286%5E2-4%281%29%28-43%29%29%29%2F2%281%29 Simplify.
r+=+%28-6%2B-sqrt%2836-%28-172%29%29%29%2F2
r+=+%28-6%2B-sqrt%28208%29%29%2F2
r+=+%28-6%2B-sqrt%2816%2A13%29%29%2F2
r+=+-3%2B4sqrt%2813%29%2F2 or r+=+-3-4sqrt%2813%29%2F2
r+=+-3%2B2sqrt%2813%29 or r+=+-3-2sqrt%2813%29