SOLUTION: v^2+3v-54=0

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Question 557653: v^2+3v-54=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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v%5E2%2B3v-54=0 Start with the given equation.


Notice that the quadratic v%5E2%2B3v-54 is in the form of Av%5E2%2BBv%2BC where A=1, B=3, and C=-54


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


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


v+=+%28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%281%29%28-54%29+%29%29%2F%282%281%29%29 Plug in A=1, B=3, and C=-54


v+=+%28-3+%2B-+sqrt%28+9-4%281%29%28-54%29+%29%29%2F%282%281%29%29 Square 3 to get 9.


v+=+%28-3+%2B-+sqrt%28+9--216+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-54%29 to get -216


v+=+%28-3+%2B-+sqrt%28+9%2B216+%29%29%2F%282%281%29%29 Rewrite sqrt%289--216%29 as sqrt%289%2B216%29


v+=+%28-3+%2B-+sqrt%28+225+%29%29%2F%282%281%29%29 Add 9 to 216 to get 225


v+=+%28-3+%2B-+sqrt%28+225+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


v+=+%28-3+%2B-+15%29%2F%282%29 Take the square root of 225 to get 15.


v+=+%28-3+%2B+15%29%2F%282%29 or v+=+%28-3+-+15%29%2F%282%29 Break up the expression.


v+=+%2812%29%2F%282%29 or v+=++%28-18%29%2F%282%29 Combine like terms.


v+=+6 or v+=+-9 Simplify.


So the solutions are v+=+6 or v+=+-9

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