SOLUTION: This is a summer assignment. I don't have a book. Solve the equation {{{ x^2 - 5x + 2 = 0 }}} thanks

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Question 150982: This is a summer assignment. I don't have a book.
Solve the equation +x%5E2+-+5x+%2B+2+=+0+
thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-5x%2B2=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-5, and c=2


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%282%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-5, and c=2


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%282%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%282%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25-8+%29%29%2F%282%281%29%29 Multiply 4%281%29%282%29 to get 8


x+=+%285+%2B-+sqrt%28+17+%29%29%2F%282%281%29%29 Subtract 8 from 25 to get 17


x+=+%285+%2B-+sqrt%28+17+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285%2Bsqrt%2817%29%29%2F%282%29 or x+=+%285-sqrt%2817%29%29%2F%282%29 Break up the expression.


So our answers are x+=+%285%2Bsqrt%2817%29%29%2F%282%29 or x+=+%285-sqrt%2817%29%29%2F%282%29


which approximate to x=4.562 or x=0.438