SOLUTION: Help with this one please! sqrt2y+7 + 4 = y I think I have to start by isolating the y to one side - is that right, and then do I subtract the 4 from both sides to cancel it

Algebra ->  Algebra  -> Radicals -> SOLUTION: Help with this one please! sqrt2y+7 + 4 = y I think I have to start by isolating the y to one side - is that right, and then do I subtract the 4 from both sides to cancel it       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 39964: Help with this one please!
sqrt2y+7 + 4 = y
I think I have to start by isolating the y to one side - is that right, and then do I subtract the 4 from both sides to cancel it out on the left?
Please show me how to figure this!

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(2y+7) + 4 = y
sqrt(2y+7)=y-4
Square both sides to get:
2y+7=y^2-8y+16
y^2-10y+9=0
(y-9(y-1)=0
y=9 or y=1
Check the answers in the original equation.
y=1 is extraneous.
Cheers,
Stan H.

Answer by Earlsdon(6099) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct...you have to get the variable y onto one side of the equation.
But you should use parentheses to clarify the problem;
Is it sqrt(2y+7) + 4 = y ?
or is it sqrt(2y) + 7 + 4 = y ?
or perhaps sqrt(2y+ 7 + 4) = y ?
I am going to assume that it's:
sqrt%282y%2B7%29+%2B+4+=+y Subtract 4 from both sides of the equation.
sqrt%282y%2B7%29+=+y+-+4 Now square both sides.
2y%2B7+=+%28y-4%29%5E2 Simplify.
2y%2B7+=+y%5E2+-+8y+%2B+16 Subtract 2y from both sides.
7+=+y%5E2+-+10y+%2B+16 Now subtract 7 from both sides.
y%5E2+-+10y+%2B+9+=+0 Solve by factoring.
%28y+-+1%29%28y+-+9%29+=+0 Apply the zero products principle.
y+-+1+=+0 and/or y+-+9+=+0
If y+-+1+=+0, then y+=+1
If y+-+9+=+0, then y+=+9
Now if youcheck these solutions by substituting y=1 and then y=9 into your original equation, you will find that y=9 works if you use only the positive value of sqrt%2825%29and y=1 works if you use only the negative value of sqrt%289%29.
sqrt%282y%2B7%29+%2B+4+=+y Try y = 3.
sqrt%282%289%29%2B7%29+%2B+4+=+9
sqrt%2818%2B7%29+%2B+4+=+9
sqrt%2825%29+%2B+4+=+9
5+%2B+4+=+9 Only the positive value of sqrt%2825%29 works.
sqrt%282y%2B7%29+%2B+4+=+y Try y = 1.
sqrt%282%281%29%2B7%29+%2B+4+=+1
sqrt%282%2B7%29+%2B+4+=+1
sqrt%289%29+%2B+4+=+1
-3+%2B+4+=+1 Only the negative value of sqrt%289%29 works.