Question 23064: -x^2-5x+1=0 can someone help with this. Thank you in advance.
Answer by eclecticist(12)   (Show Source):
You can put this solution on YOUR website! To solve this problem, which seems to have no rational roots at first, we would have to complete the square. First of all, move 1 to the right side of the equation, then factor out -1 to put it into a more simplified form.
-x^2 - 5x = -1
-(x^2 + 5x) = -1
Then, we need to add a constant to both sides of the equation to obtain a 'perfect square' for the left side of the equation. The constant we need to add is (5/2)^2, since that term would allow 'complete' the square on the left side.
-(x^2 + 5x + 25/4) = -1 - 25/4
Keep in mind that with the sign changed on the left side, 25/4 is subtracted, not added. This expression simplifies to
-(x + 5/2)^2 = -29/4
(x + 5/2)^2 = 29/4
Then take the square root of both sides, and isolate the variable.
x + 5/2 = +- sqrt(29)/2
x = -5/2 +- sqrt(29)/2
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