SOLUTION: 9000/p = 4p-20

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Question 164990: 9000/p = 4p-20
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9000%2Fp+=+4p-20 Start with the given equation.


9000+=+4p%5E2-20p Multiply EVERY term by the LCD "p" to eliminate the fraction.


0+=+4p%5E2-20p-9000 Subtract 9000 from both sides.


Notice we have a quadratic equation in the form of ap%5E2%2Bbp%2Bc where a=4, b=-20, and c=-9000


Let's use the quadratic formula to solve for p


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


p+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%284%29%28-9000%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-20, and c=-9000


p+=+%2820+%2B-+sqrt%28+%28-20%29%5E2-4%284%29%28-9000%29+%29%29%2F%282%284%29%29 Negate -20 to get 20.


p+=+%2820+%2B-+sqrt%28+400-4%284%29%28-9000%29+%29%29%2F%282%284%29%29 Square -20 to get 400.


p+=+%2820+%2B-+sqrt%28+400--144000+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-9000%29 to get -144000


p+=+%2820+%2B-+sqrt%28+400%2B144000+%29%29%2F%282%284%29%29 Rewrite sqrt%28400--144000%29 as sqrt%28400%2B144000%29


p+=+%2820+%2B-+sqrt%28+144400+%29%29%2F%282%284%29%29 Add 400 to 144000 to get 144400


p+=+%2820+%2B-+sqrt%28+144400+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


p+=+%2820+%2B-+380%29%2F%288%29 Take the square root of 144400 to get 380.


p+=+%2820+%2B+380%29%2F%288%29 or p+=+%2820+-+380%29%2F%288%29 Break up the expression.


p+=+%28400%29%2F%288%29 or p+=++%28-360%29%2F%288%29 Combine like terms.


p+=+50 or p+=+-45 Simplify.


So the answers are p+=+50 or p+=+-45