SOLUTION: 3x^2-x-5=0

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Question 568662: 3x^2-x-5=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-x-5=0 Start with the given equation.


Notice that the quadratic 3x%5E2-x-5 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-1, and C=-5


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


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


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


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%283%29%28-5%29+%29%29%2F%282%283%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%283%29%28-5%29+%29%29%2F%282%283%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--60+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-5%29 to get -60


x+=+%281+%2B-+sqrt%28+1%2B60+%29%29%2F%282%283%29%29 Rewrite sqrt%281--60%29 as sqrt%281%2B60%29


x+=+%281+%2B-+sqrt%28+61+%29%29%2F%282%283%29%29 Add 1 to 60 to get 61


x+=+%281+%2B-+sqrt%28+61+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%281%2Bsqrt%2861%29%29%2F%286%29 or x+=+%281-sqrt%2861%29%29%2F%286%29 Break up the expression.


So the solutions are x+=+%281%2Bsqrt%2861%29%29%2F%286%29 or x+=+%281-sqrt%2861%29%29%2F%286%29

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