SOLUTION: I am lost. If anyone can help I would appreciate it. Thanks Solve 3x^2-7x-11=0 Find the x intercepts of f(x)=3x^2-7x-11

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Question 129695: I am lost. If anyone can help I would appreciate it. Thanks
Solve
3x^2-7x-11=0
Find the x intercepts of
f(x)=3x^2-7x-11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Ax%5E2-7%2Ax-11=0 ( notice a=3, b=-7, and c=-11)





x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A3%2A-11+%29%29%2F%282%2A3%29 Plug in a=3, b=-7, and c=-11




x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A3%2A-11+%29%29%2F%282%2A3%29 Negate -7 to get 7




x+=+%287+%2B-+sqrt%28+49-4%2A3%2A-11+%29%29%2F%282%2A3%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)




x+=+%287+%2B-+sqrt%28+49%2B132+%29%29%2F%282%2A3%29 Multiply -4%2A-11%2A3 to get 132




x+=+%287+%2B-+sqrt%28+181+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%287+%2B-+sqrt%28181%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%287+%2B-+sqrt%28181%29%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%287+%2B+sqrt%28181%29%29%2F6 or x+=+%287+-+sqrt%28181%29%29%2F6



Now break up the fraction



x=%2B7%2F6%2Bsqrt%28181%29%2F6 or x=%2B7%2F6-sqrt%28181%29%2F6



Simplify



x=7%2F6%2Bsqrt%28181%29%2F6 or x=7%2F6-sqrt%28181%29%2F6



So the solutions are:

x=7%2F6%2Bsqrt%28181%29%2F6 or x=7%2F6-sqrt%28181%29%2F6