SOLUTION: square root x + 63 + 9 = x

Algebra ->  Radicals -> SOLUTION: square root x + 63 + 9 = x      Log On


   

Question 130152: square root x + 63 + 9 = x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x+%2B+63%29+%2B+9+=+x Start with the given equation


sqrt%28x+%2B+63%29+=+x-9 Subtract 9 from both sides


x%2B63+=+%28x-9%29%5E2 Square both sides


x%2B63+=+x%5E2-18x%2B81 Foil



0=x%5E2-18x%2B81-x-63 Subtract x from both sides. Subtract 63 from both sides.

0=x%5E2-19x%2B18 Combine like terms


0=%28x-18%29%28x-1%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-18=0 or x-1=0

x=18 or x=1 Now solve for x in each case


So our possible solutions are
x=18 or x=1


Now let's check our possible solutions


Let's check the first solution x=18

sqrt%28x+%2B+63%29+%2B+9+=+x Start with the given equation}}} Start with the given equation


sqrt%2818+%2B+63%29+%2B+9+=+18 Plug in x=18.


sqrt%2881%29+%2B+9+=+18 Add


9+%2B+9+=+18 Take the square root of 81 to get 9


18+=+18 Add. Since the two sides of the equation are equal, this verifies the solution x=18.



--------------------------


Let's check the first solution x=1

sqrt%28x+%2B+63%29+%2B+9+=+x Start with the given equation}}} Start with the given equation


sqrt%281+%2B+63%29+%2B+9+=+1 Plug in x=1.


sqrt%2864%29+%2B+9+=+1 Add


8+%2B+9+=+18 Take the square root of 64 to get 8


17+=+18 Add. Since the two sides of the equation are not equal, this means that x=1 is an extraneous solution




-----------------------------

Answer:


So our only solution is x=18