SOLUTION: Find the roots of 2x to the second power-5x+1=0

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Question 111852: Find the roots of 2x to the second power-5x+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%5E2-5%2Ax%2B1=0 ( notice a=2, b=-5, and c=1)





x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 Plug in a=2, b=-5, and c=1




x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 Negate -5 to get 5




x+=+%285+%2B-+sqrt%28+25-4%2A2%2A1+%29%29%2F%282%2A2%29 Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because %28-5%29%5E2=-5%2A-5=25.)




x+=+%285+%2B-+sqrt%28+25%2B-8+%29%29%2F%282%2A2%29 Multiply -4%2A1%2A2 to get -8




x+=+%285+%2B-+sqrt%28+17+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%285+%2B-+sqrt%2817%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+=+%285+%2B-+sqrt%2817%29%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%285+%2B+sqrt%2817%29%29%2F4 or x+=+%285+-+sqrt%2817%29%29%2F4



Now break up the fraction



x=%2B5%2F4%2Bsqrt%2817%29%2F4 or x=%2B5%2F4-sqrt%2817%29%2F4



Simplify



x=5%2F4%2Bsqrt%2817%29%2F4 or x=5%2F4-sqrt%2817%29%2F4



So the solutions are:

x=5%2F4%2Bsqrt%2817%29%2F4 or x=5%2F4-sqrt%2817%29%2F4