SOLUTION: Solve equation using quadratic formula: 3n^2 - 2n - 56 = 0 (Three n squared minus 2n minus 56 equals 0)

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Question 502785: Solve equation using quadratic formula:
3n^2 - 2n - 56 = 0
(Three n squared minus 2n minus 56 equals 0)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3n%5E2-2n-56=0 Start with the given equation.


Notice that the quadratic 3n%5E2-2n-56 is in the form of An%5E2%2BBn%2BC where A=3, B=-2, and C=-56


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


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


n+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%28-56%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-2, and C=-56


n+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%28-56%29+%29%29%2F%282%283%29%29 Negate -2 to get 2.


n+=+%282+%2B-+sqrt%28+4-4%283%29%28-56%29+%29%29%2F%282%283%29%29 Square -2 to get 4.


n+=+%282+%2B-+sqrt%28+4--672+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-56%29 to get -672


n+=+%282+%2B-+sqrt%28+4%2B672+%29%29%2F%282%283%29%29 Rewrite sqrt%284--672%29 as sqrt%284%2B672%29


n+=+%282+%2B-+sqrt%28+676+%29%29%2F%282%283%29%29 Add 4 to 672 to get 676


n+=+%282+%2B-+sqrt%28+676+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


n+=+%282+%2B-+26%29%2F%286%29 Take the square root of 676 to get 26.


n+=+%282+%2B+26%29%2F%286%29 or n+=+%282+-+26%29%2F%286%29 Break up the expression.


n+=+%2828%29%2F%286%29 or n+=++%28-24%29%2F%286%29 Combine like terms.


n+=+14%2F3 or n+=+-4 Simplify.


So the solutions are n+=+14%2F3 or n+=+-4