# SOLUTION: solve. sqrt of x+7 + sqrt of x+16 =19 thak you.

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 Question 63352: solve. sqrt of x+7 + sqrt of x+16 =19 thak you.Answer by ptaylor(2048)   (Show Source): You can put this solution on YOUR website!To solve: sqrt(x+7)+sqrt(x+16)=19 We'll start getting rid of the radicals by squaring both sides of the equation but first lets move one of the radicals to the right side of the equation by subtracting sqrt(x+16) from both sides. I think this will make the problem slightly easier. We will get: sqrt(x+7)=19-sqrt(x+16) now we'll square both sides and we have: x+7=361-38sqrt(x+16)+(x+16) now lets collect like terms and, at the same time, isolate the remaining radical on the right side of the equation. We get: x-x+7-361-16=-38sqrt(x+16)simplifying: -370=-38sqrt(x+16) Just to simplify more, we'll divide both sides by -2 and get: 185=19sqrt(x+16) Now we'll square both sides again and we have: 34,225=361(x+16)=361x+(361)(16)=361x+5776 simplifying 361x=34,225-5776 or 361x=28,449 and x=78.8 You can check my calculations for accuracy but this is my general approach when dealing with radicals. Hope this helps and have a nice holiday season---ptaylor