SOLUTION: 5y(y + 9) = 6(y + 9)

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Question 241759: 5y(y + 9) = 6(y + 9)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5y%28y+%2B+9%29+=+6%28y+%2B+9%29 Start with the given equation.


5y%5E2%2B45y+=+6y+%2B+54 Distribute


5y%5E2%2B45y-6y-54=0 Get every term to the left side.


5y%5E2%2B39y-54=0 Combine like terms.


Notice that the quadratic 5y%5E2%2B39y-54 is in the form of Ay%5E2%2BBy%2BC where A=5, B=39, and C=-54


Let's use the quadratic formula to solve for "y":


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%2839%29+%2B-+sqrt%28+%2839%29%5E2-4%285%29%28-54%29+%29%29%2F%282%285%29%29 Plug in A=5, B=39, and C=-54


y+=+%28-39+%2B-+sqrt%28+1521-4%285%29%28-54%29+%29%29%2F%282%285%29%29 Square 39 to get 1521.


y+=+%28-39+%2B-+sqrt%28+1521--1080+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-54%29 to get -1080


y+=+%28-39+%2B-+sqrt%28+1521%2B1080+%29%29%2F%282%285%29%29 Rewrite sqrt%281521--1080%29 as sqrt%281521%2B1080%29


y+=+%28-39+%2B-+sqrt%28+2601+%29%29%2F%282%285%29%29 Add 1521 to 1080 to get 2601


y+=+%28-39+%2B-+sqrt%28+2601+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


y+=+%28-39+%2B-+51%29%2F%2810%29 Take the square root of 2601 to get 51.


y+=+%28-39+%2B+51%29%2F%2810%29 or y+=+%28-39+-+51%29%2F%2810%29 Break up the expression.


y+=+%2812%29%2F%2810%29 or y+=++%28-90%29%2F%2810%29 Combine like terms.


y+=+6%2F5 or y+=+-9 Simplify.


So the solutions are y+=+6%2F5 or y+=+-9