SOLUTION: 2x^2-9x+9=0

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Question 273326: 2x^2-9x+9=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For more help, check out this quadratic formula solver.


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%5E2-9%2Ax%2B9=0 ( notice a=2, b=-9, and c=9)





x+=+%28--9+%2B-+sqrt%28+%28-9%29%5E2-4%2A2%2A9+%29%29%2F%282%2A2%29 Plug in a=2, b=-9, and c=9




x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%2A2%2A9+%29%29%2F%282%2A2%29 Negate -9 to get 9




x+=+%289+%2B-+sqrt%28+81-4%2A2%2A9+%29%29%2F%282%2A2%29 Square -9 to get 81 (note: remember when you square -9, you must square the negative as well. This is because %28-9%29%5E2=-9%2A-9=81.)




x+=+%289+%2B-+sqrt%28+81%2B-72+%29%29%2F%282%2A2%29 Multiply -4%2A9%2A2 to get -72




x+=+%289+%2B-+sqrt%28+9+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%289+%2B-+3%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%289+%2B-+3%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%289+%2B+3%29%2F4 or x+=+%289+-+3%29%2F4


Lets look at the first part:


x=%289+%2B+3%29%2F4


x=12%2F4 Add the terms in the numerator

x=3 Divide


So one answer is

x=3




Now lets look at the second part:


x=%289+-+3%29%2F4


x=6%2F4 Subtract the terms in the numerator

x=3%2F2 Divide


So another answer is

x=3%2F2