SOLUTION: Alright here is a tough one that I have been trying for an hour and can't seem to figure out. (x-6)^2+(51-x)^2=9 Problem seemed easy enough but I can't see to solve for x and w

Algebra ->  Radicals -> SOLUTION: Alright here is a tough one that I have been trying for an hour and can't seem to figure out. (x-6)^2+(51-x)^2=9 Problem seemed easy enough but I can't see to solve for x and w      Log On


   

Question 155287: Alright here is a tough one that I have been trying for an hour and can't seem to figure out.
(x-6)^2+(51-x)^2=9
Problem seemed easy enough but I can't see to solve for x and when I isolate an equation on one side I end up getting huge numbers that are unworkable
Thanks for the help
Found 3 solutions by checkley77, Earlsdon, scott8148:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(x-6)^2+(51-x)^2=9
x^2-12x+36+2601-102x+x^2=9
2x^2-114x+2637-9=0
2x62-114x+2628=0
2(x^2-57x+1314)=0
Using the quadratic equation:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ we get:
x=(57+-sqrt[-57^2-4*1*1314])/281
x=(57+-sqrt[3249-5256])/2
x=(57+-sqrt[-2007])/2
x=(57+-44.8i)/2
x=57/2+-44.8i/2
x=28.5+-22.4i answer.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%28x-6%29%5E2%2B%2851-x%29%5E2+=+9 Simplify.
%28x%5E2-12x%2B36%29%2B%282601-102x%2Bx%5E2%29+=+9 Combine like-terms.
2x%5E2-114x%2B2637+=+9 Subtract 9 from both sides.
2x%5E2-114x%2B2628+=+0 Factor out a 2.
2%28x%5E2-57x%2B1314%29+=+0, so...
x%5E2-57x%2B1314+=+0 Use the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a Here, a = 1, b = -57, and c = 1314
x+=+%28-%28-57%29%2B-sqrt%28%28-57%29%5E2-4%281%29%281314%29%29%29%2F2%281%29 Simplify.
x+=+%2857%2B-sqrt%283249-5256%29%29%2F2
x+=+%2857%2B-sqrt%28-2007%29%29%2F2
x+=+%2857%2B3sqrt%28-223%29%29%2F2 or x+=+%2857-3sqrt%28-223%29%29%2F2
If you need the approximate answers, take the square roots as indicated:
x+=+28.5%2B22.4i or x+=+28.5-22.4i

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
FOILing __ x^2-12x+36+2601-102x+x^2=9 __ subtracting 9 __ 2x^2-114x+2628=0 __ dividing by 2 __ x^2-57x+1314=0

not factorable __ use quadratic formula to find x