SOLUTION: 7X2-17X+6=O

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Question 101479: 7X2-17X+6=O
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 7%2Ax%5E2-17%2Ax%2B6=0 ( notice a=7, b=-17, and c=6)





x+=+%28--17+%2B-+sqrt%28+%28-17%29%5E2-4%2A7%2A6+%29%29%2F%282%2A7%29 Plug in a=7, b=-17, and c=6




x+=+%2817+%2B-+sqrt%28+%28-17%29%5E2-4%2A7%2A6+%29%29%2F%282%2A7%29 Negate -17 to get 17




x+=+%2817+%2B-+sqrt%28+289-4%2A7%2A6+%29%29%2F%282%2A7%29 Square -17 to get 289 (note: remember when you square -17, you must square the negative as well. This is because %28-17%29%5E2=-17%2A-17=289.)




x+=+%2817+%2B-+sqrt%28+289%2B-168+%29%29%2F%282%2A7%29 Multiply -4%2A6%2A7 to get -168




x+=+%2817+%2B-+sqrt%28+121+%29%29%2F%282%2A7%29 Combine like terms in the radicand (everything under the square root)




x+=+%2817+%2B-+11%29%2F%282%2A7%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2817+%2B-+11%29%2F14 Multiply 2 and 7 to get 14


So now the expression breaks down into two parts


x+=+%2817+%2B+11%29%2F14 or x+=+%2817+-+11%29%2F14


Lets look at the first part:


x=%2817+%2B+11%29%2F14


x=28%2F14 Add the terms in the numerator

x=2 Divide


So one answer is

x=2




Now lets look at the second part:


x=%2817+-+11%29%2F14


x=6%2F14 Subtract the terms in the numerator

x=3%2F7 Divide


So another answer is

x=3%2F7


So our solutions are:

x=2 or x=3%2F7