SOLUTION: what is the quadratic formula for 2x^2 - 11x - 1 = 0

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Question 228745: what is the quadratic formula for 2x^2 - 11x - 1 = 0
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 2%2Ax%5E2-11%2Ax-1=0 ( notice a=2, b=-11, and c=-1)





x+=+%28--11+%2B-+sqrt%28+%28-11%29%5E2-4%2A2%2A-1+%29%29%2F%282%2A2%29 Plug in a=2, b=-11, and c=-1




x+=+%2811+%2B-+sqrt%28+%28-11%29%5E2-4%2A2%2A-1+%29%29%2F%282%2A2%29 Negate -11 to get 11




x+=+%2811+%2B-+sqrt%28+121-4%2A2%2A-1+%29%29%2F%282%2A2%29 Square -11 to get 121 (note: remember when you square -11, you must square the negative as well. This is because %28-11%29%5E2=-11%2A-11=121.)




x+=+%2811+%2B-+sqrt%28+121%2B8+%29%29%2F%282%2A2%29 Multiply -4%2A-1%2A2 to get 8




x+=+%2811+%2B-+sqrt%28+129+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%2811+%2B-+sqrt%28129%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2811+%2B-+sqrt%28129%29%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%2811+%2B+sqrt%28129%29%29%2F4 or x+=+%2811+-+sqrt%28129%29%29%2F4



Now break up the fraction



x=%2B11%2F4%2Bsqrt%28129%29%2F4 or x=%2B11%2F4-sqrt%28129%29%2F4



Simplify



x=11%2F4%2Bsqrt%28129%29%2F4 or x=11%2F4-sqrt%28129%29%2F4



So the solutions are:

x=11%2F4%2Bsqrt%28129%29%2F4 or x=11%2F4-sqrt%28129%29%2F4