SOLUTION: 3x to the power of 2-16x+5=0

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Question 760684: 3x to the power of 2-16x+5=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 3%2Ax%5E2-16%2Ax%2B5=0 ( notice a=3, b=-16, and c=5)





x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A3%2A5+%29%29%2F%282%2A3%29 Plug in a=3, b=-16, and c=5




x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A3%2A5+%29%29%2F%282%2A3%29 Negate -16 to get 16




x+=+%2816+%2B-+sqrt%28+256-4%2A3%2A5+%29%29%2F%282%2A3%29 Square -16 to get 256 (note: remember when you square -16, you must square the negative as well. This is because %28-16%29%5E2=-16%2A-16=256.)




x+=+%2816+%2B-+sqrt%28+256%2B-60+%29%29%2F%282%2A3%29 Multiply -4%2A5%2A3 to get -60




x+=+%2816+%2B-+sqrt%28+196+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%2816+%2B-+14%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2816+%2B-+14%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%2816+%2B+14%29%2F6 or x+=+%2816+-+14%29%2F6


Lets look at the first part:


x=%2816+%2B+14%29%2F6


x=30%2F6 Add the terms in the numerator

x=5 Divide


So one answer is

x=5




Now lets look at the second part:


x=%2816+-+14%29%2F6


x=2%2F6 Subtract the terms in the numerator

x=1%2F3 Divide


So another answer is

x=1%2F3


So our solutions are:

x=5 or x=1%2F3