SOLUTION: Solve 2y(y+8)=7(y+8) Find smaller and larger value

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Question 338326: Solve
Find smaller and larger value

Answer by jim_thompson5910(33401) About Me  (Show Source):
You can put this solution on YOUR website!
2y%28y%2B8%29=7%28y%2B8%29 Start with the given equation.

2y%5E2%2B16y=7y%2B56 Distribute.

2y%5E2%2B16y-7y-56=0 Get every term to the left side.

2y%5E2%2B9y-56=0 Combine like terms.

Notice that the quadratic 2y%5E2%2B9y-56 is in the form of Ay%5E2%2BBy%2BC where A=2, B=9, and C=-56

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-%289%29+%2B-+sqrt%28+%289%29%5E2-4%282%29%28-56%29+%29%29%2F%282%282%29%29 Plug in A=2, B=9, and C=-56

y+=+%28-9+%2B-+sqrt%28+81-4%282%29%28-56%29+%29%29%2F%282%282%29%29 Square 9 to get 81.

y+=+%28-9+%2B-+sqrt%28+81--448+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-56%29 to get -448

y+=+%28-9+%2B-+sqrt%28+81%2B448+%29%29%2F%282%282%29%29 Rewrite sqrt%2881--448%29 as sqrt%2881%2B448%29

y+=+%28-9+%2B-+sqrt%28+529+%29%29%2F%282%282%29%29 Add 81 to 448 to get 529

y+=+%28-9+%2B-+sqrt%28+529+%29%29%2F%284%29 Multiply 2 and 2 to get 4.

y+=+%28-9+%2B-+23%29%2F%284%29 Take the square root of 529 to get 23.

y+=+%28-9+%2B+23%29%2F%284%29 or y+=+%28-9+-+23%29%2F%284%29 Break up the expression.

y+=+%2814%29%2F%284%29 or y+=++%28-32%29%2F%284%29 Combine like terms.

y+=+7%2F2 or y+=+-8 Simplify.

So the solutions are y+=+7%2F2 or y+=+-8

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