SOLUTION: Solve square root of 2y+7 +4=y

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Question 118090: Solve
square root of 2y+7 +4=y
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

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


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%2B16Foil the right side


0=y%5E2-10y%2B9 Subtract 2y and 7 from both sides



%28y-9%29%28y-1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
y-9=0 or y-1=0

y=9 or y=1 Now solve for y in each case


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

Check:
Let's check the possible solution 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 of 25 to get 5

9=9 Add. Since the two sides of the equation are equal, this verifies our answer.


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Let's check the possible solution 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=1 Add

3%2B4=1 Take the square root of 25 to get 5

9=1 Add. Since the two sides of the equation are not equal, this means that y=1 is not a valid solution.



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So the only solution is y=9