SOLUTION: y-2-8 sqrt(y-2)+15=0

Algebra ->  Functions -> SOLUTION: y-2-8 sqrt(y-2)+15=0      Log On


   

Question 151318: y-2-8 sqrt(y-2)+15=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y-2-8%2Asqrt%28y-2%29%2B15=0 Start with the given equation.


y-8%2Asqrt%28y-2%29%2B13=0 Combine like terms.


y-8%2Asqrt%28y-2%29=-13 Subtract 13 from both sides.


-8%2Asqrt%28y-2%29=-13-y Subtract y from both sides.


64%28y-2%29=%28-13-y%29%5E2 Square both sides.


64%28y-2%29=169%2B26y%2By%5E2 FOIL


64y-128=169%2B26y%2By%5E2 Distribute


0=169%2B26y%2By%5E2-64y%2B128 Subtract 64y from both sides. Add 128 to both sides.


0=y%5E2-38y%2B297 Combine like terms


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=1, b=-38, and c=297


Let's use the quadratic formula to solve for y


y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


y+=+%28-%28-38%29+%2B-+sqrt%28+%28-38%29%5E2-4%281%29%28297%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-38, and c=297


y+=+%2838+%2B-+sqrt%28+%28-38%29%5E2-4%281%29%28297%29+%29%29%2F%282%281%29%29 Negate -38 to get 38.


y+=+%2838+%2B-+sqrt%28+1444-4%281%29%28297%29+%29%29%2F%282%281%29%29 Square -38 to get 1444.


y+=+%2838+%2B-+sqrt%28+1444-1188+%29%29%2F%282%281%29%29 Multiply 4%281%29%28297%29 to get 1188


y+=+%2838+%2B-+sqrt%28+256+%29%29%2F%282%281%29%29 Subtract 1188 from 1444 to get 256


y+=+%2838+%2B-+sqrt%28+256+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%2838+%2B-+16%29%2F%282%29 Take the square root of 256 to get 16.


y+=+%2838+%2B+16%29%2F%282%29 or y+=+%2838+-+16%29%2F%282%29 Break up the expression.


y+=+%2854%29%2F%282%29 or y+=++%2822%29%2F%282%29 Combine like terms.


y+=+27 or y+=+11 Simplify.


So our answers are y+=+27 or y+=+11