SOLUTION: solve, step by step √(x+5)+√(2x+3)=9 √=square root ( )=what is under the square roots

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Question 186671: solve, step by step √(x+5)+√(2x+3)=9
√=square root
( )=what is under the square roots
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B5%29%2Bsqrt%282x%2B3%29=9 Start with the given equation.


sqrt%28x%2B5%29=9-sqrt%282x%2B3%29 Subtract sqrt%282x%2B3%29 from both sides.


x%2B5=%289-sqrt%282x%2B3%29%29%5E2 Square both sides


x%2B5=81-18%2Asqrt%282x%2B3%29%2B2x%2B3 FOIL


x%2B5=84%2B2x-18%2Asqrt%282x%2B3%29 Combine like terms.


x%2B5-84-2x=-18%2Asqrt%282x%2B3%29 Subtract 84 from both sides. Subtract 2x from both sides.


-x-79=-18%2Asqrt%282x%2B3%29 Combine like terms.


%28-x-79%29%5E2=%28-18%2Asqrt%282x%2B3%29%29%5E2 Square both sides


x%5E2%2B158x%2B6241=324%2A%282x%2B3%29 FOIL and square the right side


x%5E2%2B158x%2B6241=648x%2B972 Distribute


x%5E2%2B158x%2B6241-648x-972=0 Get everything to the left side.


x%5E2-490x%2B5269=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-490, and c=5269


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-490%29+%2B-+sqrt%28+%28-490%29%5E2-4%281%29%285269%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-490, and c=5269


x+=+%28490+%2B-+sqrt%28+%28-490%29%5E2-4%281%29%285269%29+%29%29%2F%282%281%29%29 Negate -490 to get 490.


x+=+%28490+%2B-+sqrt%28+240100-4%281%29%285269%29+%29%29%2F%282%281%29%29 Square -490 to get 240100.


x+=+%28490+%2B-+sqrt%28+240100-21076+%29%29%2F%282%281%29%29 Multiply 4%281%29%285269%29 to get 21076


x+=+%28490+%2B-+sqrt%28+219024+%29%29%2F%282%281%29%29 Subtract 21076 from 240100 to get 219024


x+=+%28490+%2B-+sqrt%28+219024+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28490+%2B-+468%29%2F%282%29 Take the square root of 219024 to get 468.


x+=+%28490+%2B+468%29%2F%282%29 or x+=+%28490+-+468%29%2F%282%29 Break up the expression.


x+=+%28958%29%2F%282%29 or x+=++%2822%29%2F%282%29 Combine like terms.


x+=+479 or x+=+11 Simplify.


So the possible answers are x+=+479 or x+=+11



However, if you plug in x+=+479, the original equation will NOT be true. So x+=+479 is NOT a solution



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Answer:

So the solution is x+=+11