SOLUTION: Solve and check solution sqrt (2y + 7) + 4 = y Thank You!!!

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Question 46370: Solve and check solution

sqrt (2y + 7) + 4 = y

Thank You!!!
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Solve and check:
sqrt%282y%2B7%29%2B4+=+y Subtract 4 from both sides.
sqrt%282y%2B7%29+=+y-4 Now square both sides.(Caution! Squaring may introduce an extraneous root)
2y%2B7+=+y%5E2-8y%2B16 Collect like-terms.
y%5E2-10y%2B9+=+0 Solve by factoring.
%28y-9%29%28y-1%29+=+0 Apply the zero products principle.
y-9+=+0 and/or y-1+=+0
The roots are(?):
y = 9
y = 1
Check y=9
sqrt%282%289%29%2B7%29%2B4+=+sqrt%2825%29%2B4 = 5%2B4+=+9 Checks! or -5%2B4+=+-1
The last solution is an extraneous solution introduced by squaring. Remember thatsqrt%2825%29+=+%2B5 or -5
Check y=1
sqrt%282%281%29%2B7%29%2B4+=+sqrt%289%29%2B4 = 3%2B4+=+7 or -3%2B4+=+1 The first solution doesn't check. Extraneous solution was introduced when squaring during the solving process.