SOLUTION: Can someone explain how to solve the following problem? 2x^2 + 1 = 5x

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Question 275248: Can someone explain how to solve the following problem?
2x^2 + 1 = 5x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B1=5x Start with the given equation.


2x%5E2-5x%2B1=0 Subtract 5x from both sides.


Notice that the quadratic 2x%5E2-5x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=2, B=-5, and C=1


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%282%29%281%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-5, and C=1


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


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


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


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


x+=+%285+%2B-+sqrt%28+17+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%285%2Bsqrt%2817%29%29%2F%284%29 or x+=+%285-sqrt%2817%29%29%2F%284%29 Break up the expression.


So the solutions are x+=+%285%2Bsqrt%2817%29%29%2F%284%29 or x+=+%285-sqrt%2817%29%29%2F%284%29