SOLUTION: Can you help me solve this equation? sqrt 2y+7 + 4 = y The 2y+7 is in the radical sign Thanks

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Question 39890: Can you help me solve this equation?
sqrt 2y+7 + 4 = y
The 2y+7 is in the radical sign
Thanks
Found 2 solutions by fractalier, junior403:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
First we isolate the radical and then square both sides...so from
sqrt(2y+7) + 4 = y
sqrt(2y+7) = y - 4
2y + 7 = (y - 4)^2
2y + 7 = y^2 - 8y + 16 now collect like terms and solve
y^2 - 10y + 9 = 0
(y-9)(y-1) = 0
y = 9 or y = 1
Yo have to check these, however, and only y = 9 checks out. y = 1 doesn't check. Thus,
y = 9

Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
let's see...
%28sqrt%28+2y%2B7+%29%29+%2B+4+=+y+
First we need to isolate the radical...
So we can subtract 4 from both sides of the equation...
%28sqrt%28+2y%2B7+%29%29+=+y+-+4+
Then, in order to eliminate the radical sign, we need to square both sides...
%28sqrt%28+2y%2B7+%29%29%5E2+=+%28y+-+4%29%5E2+
The square root of a squared number, is just that number so...
+2y%2B7+=+%28y+-+4%29%5E2+
Now we can work on the other side by distributing the power of 2...
+2y%2B7+=+y%5E2+%2B+16+
Now we can write the quadratic equation in standard form on one side of the equation and equal to zero by subtracting the 2y and the 7 from both sides...
+y%5E2+-+2y+%2B+9+=+0+
Now we can solve this equation using the quadratic formula...
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Now we simply insert the coefficients of our equation such that a=1 b=-2 c=9...
y+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+
and solve...
y+=+%282+%2B-+sqrt%28+4+-+36+%29%29%2F%282%29+
and...
y+=+%282+%2B-+sqrt%28+-+32+%29%29%2F%282%29+
use imaginary numbers to sove for a negative square root...
y+=+%282+%2B-+i%29+sqrt%28+32+%29%2F%282%29+
or...
y+=+%282+%2B-+i%29+sqrt%28+16%2A2+%29%2F%282%29+
the square root of 16 is 4 so that can come out from under the radical...
y+=+%282+%2B-+4i%29+sqrt%28+2+%29%2F%282%29+
Now we can factor out a 2 from the numerator in order to cancel out the 2 in the denominator...
y+=+2%281+%2B-+2i%29+sqrt%28+2+%29%2F%282%29+
Which can be simplified as...
y+=+%281+%2B-+2i%29+sqrt%28+2+%29
This is your answer in its simplist form.
So the solution set would be...
%281+%2B+2i%29+sqrt%28+2+%29,%281+-+2i%29+sqrt%28+2+%29
I hope this helps
Good Luck!