SOLUTION: Hi. I'm trying to solve x^2-5x+6=0. Thank you.

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Question 273348: Hi. I'm trying to solve x^2-5x+6=0. Thank you.
Found 2 solutions by jim_thompson5910, solver91311:
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 x%5E2-5%2Ax%2B6=0 ( notice a=1, b=-5, and c=6)





x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29 Plug in a=1, b=-5, and c=6




x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29 Negate -5 to get 5




x+=+%285+%2B-+sqrt%28+25-4%2A1%2A6+%29%29%2F%282%2A1%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-24+%29%29%2F%282%2A1%29 Multiply -4%2A6%2A1 to get -24




x+=+%285+%2B-+sqrt%28+1+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%285+%2B-+1%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%285+%2B-+1%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%285+%2B+1%29%2F2 or x+=+%285+-+1%29%2F2


Lets look at the first part:


x=%285+%2B+1%29%2F2


x=6%2F2 Add the terms in the numerator

x=3 Divide


So one answer is

x=3




Now lets look at the second part:


x=%285+-+1%29%2F2


x=4%2F2 Subtract the terms in the numerator

x=2 Divide


So another answer is

x=2


So our solutions are:

x=3 or x=2

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let's start with a hint:





Let me know if that does it for you or if you need more help.

John