SOLUTION: solve the radical equation check your solutions /2y+7+4=y

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Question 97129: solve the radical equation check your solutions
/2y+7+4=y
Found 2 solutions by Nate, jim_thompson5910:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282y+%2B+7%29+%2B+4+=+y
sqrt%282y+%2B+7%29+=+y+-+4
2y+%2B+7+=+%28y+-+4%29%5E2
2y+%2B+7+=+y%5E2+-+8y+%2B+16
0+=+y%5E2+-+10y+%2B+9
0+=+%28y+-+9%29%28y+-+1%29
y = 9 and y = 1
y = 1 doesn't work ... y = 9 is the only answer

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282y%2B7%29%2B4=y Your problem looks like this right?


sqrt%282y%2B7%29=y-4 Subtract 4 from both sides


2y%2B7=%28y-4%29%5E2 Square both sides


2y%2B7=y%5E2-8y%2B16 Foil


0=y%5E2-10y%2B9 Get all terms to one side




Let's use the quadratic formula to solve for y:


Starting with the general quadratic

ay%5E2%2Bby%2Bc=0

the general solution using the quadratic equation is:

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve y%5E2-10%2Ay%2B9=0 ( notice a=1, b=-10, and c=9)

y+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29 Plug in a=1, b=-10, and c=9



y+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29 Negate -10 to get 10



y+=+%2810+%2B-+sqrt%28+100-4%2A1%2A9+%29%29%2F%282%2A1%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)



y+=+%2810+%2B-+sqrt%28+100%2B-36+%29%29%2F%282%2A1%29 Multiply -4%2A9%2A1 to get -36



y+=+%2810+%2B-+sqrt%28+64+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



y+=+%2810+%2B-+8%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



y+=+%2810+%2B-+8%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

y+=+%2810+%2B+8%29%2F2 or y+=+%2810+-+8%29%2F2

Lets look at the first part:

x=%2810+%2B+8%29%2F2

y=18%2F2 Add the terms in the numerator
y=9 Divide

So one answer is
y=9



Now lets look at the second part:

x=%2810+-+8%29%2F2

y=2%2F2 Subtract the terms in the numerator
y=1 Divide

So another answer is
y=1

So our possible solutions are:
y=9 or y=1


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Now we have to check our answers:

Lets check y=9


sqrt%282y%2B7%29%2B4=y Start with the given equation


sqrt%282%289%29%2B7%29%2B4=9 Plug in y=9

sqrt%2818%2B7%29%2B4=9 Multiply


sqrt%2825%29%2B4=9 Add


5%2B4=9 Take the square root


9=9 Add. Since the equation is true, y=9 is a solution




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


Lets check y=1


sqrt%282y%2B7%29%2B4=y Start with the given equation


sqrt%282%281%29%2B7%29%2B4=1 Plug in y=1

sqrt%282%2B7%29%2B4=1 Multiply


sqrt%289%29%2B4=9 Add


3%2B4=9 Take the square root


7=9 Add. Since the equation is not true, y=1 is a not a solution




Answer:

So our only solution is y=9