SOLUTION: how do you solve the equation 4p^2-90=-9p?

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Question 566230: how do you solve the equation 4p^2-90=-9p?
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!

4p%5E2-90=-9p Start with the given equation.


4p%5E2-90%2B9p=0 Get every term to the left side.


4p%5E2%2B9p-90=0 Rearrange the terms.


Notice that the quadratic 4p%5E2%2B9p-90 is in the form of Ap%5E2%2BBp%2BC where A=4, B=9, and C=-90


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-%289%29+%2B-+sqrt%28+%289%29%5E2-4%284%29%28-90%29+%29%29%2F%282%284%29%29 Plug in A=4, B=9, and C=-90


p+=+%28-9+%2B-+sqrt%28+81-4%284%29%28-90%29+%29%29%2F%282%284%29%29 Square 9 to get 81.


p+=+%28-9+%2B-+sqrt%28+81--1440+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-90%29 to get -1440


p+=+%28-9+%2B-+sqrt%28+81%2B1440+%29%29%2F%282%284%29%29 Rewrite sqrt%2881--1440%29 as sqrt%2881%2B1440%29


p+=+%28-9+%2B-+sqrt%28+1521+%29%29%2F%282%284%29%29 Add 81 to 1440 to get 1521


p+=+%28-9+%2B-+sqrt%28+1521+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


p+=+%28-9+%2B-+39%29%2F%288%29 Take the square root of 1521 to get 39.


p+=+%28-9+%2B+39%29%2F%288%29 or p+=+%28-9+-+39%29%2F%288%29 Break up the expression.


p+=+%2830%29%2F%288%29 or p+=++%28-48%29%2F%288%29 Combine like terms.


p+=+15%2F4 or p+=+-6 Simplify.


So the solutions are p+=+15%2F4 or p+=+-6