SOLUTION: help me solve {{{ sqrt(6y+4)+6=y }}}

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Question 538704: help me solve +sqrt%286y%2B4%29%2B6=y+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

+sqrt%286y%2B4%29%2B6=y+ Start with the given equation.

+sqrt%286y%2B4%29=y-6+ Subtract 6 from both sides.

+%28sqrt%286y%2B4%29%29%5E2=%28y-6%29%5E2+ Square both sides

+6y%2B4=y%5E2-12y%2B36+ Square and FOIL

+0=y%5E2-12y%2B36-6y-4+ Get everything to one side

+0=y%5E2-18y%2B32+ Combine like terms.

+y%5E2-18y%2B32=0+ Flip the equation


Notice that the quadratic y%5E2-18y%2B32 is in the form of Ay%5E2%2BBy%2BC where A=1, B=-18, and C=32


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-%28-18%29+%2B-+sqrt%28+%28-18%29%5E2-4%281%29%2832%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-18, and C=32


y+=+%2818+%2B-+sqrt%28+%28-18%29%5E2-4%281%29%2832%29+%29%29%2F%282%281%29%29 Negate -18 to get 18.


y+=+%2818+%2B-+sqrt%28+324-4%281%29%2832%29+%29%29%2F%282%281%29%29 Square -18 to get 324.


y+=+%2818+%2B-+sqrt%28+324-128+%29%29%2F%282%281%29%29 Multiply 4%281%29%2832%29 to get 128


y+=+%2818+%2B-+sqrt%28+196+%29%29%2F%282%281%29%29 Subtract 128 from 324 to get 196


y+=+%2818+%2B-+sqrt%28+196+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%2818+%2B-+14%29%2F%282%29 Take the square root of 196 to get 14.


y+=+%2818+%2B+14%29%2F%282%29 or y+=+%2818+-+14%29%2F%282%29 Break up the expression.


y+=+%2832%29%2F%282%29 or y+=++%284%29%2F%282%29 Combine like terms.


y+=+16 or y+=+2 Simplify.


So the possible solutions are y+=+16 or y+=+2


However, when doing the check (which I'll let you do), you'll find that only y=16 works.


So y=16 is the only solution.


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim