Question 884339: Solve equation:
x^2+2x-1=0
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Given:
(1) x^2 + 2x -1 = 0
You can use the quadratic equation or complete the square, as follows
(2) (x + 1)^2 = x^2 + 2x +1 or
(3) x^2 + 2x = (x+1)^2 - 1
Now put (3) into (1) to get
(4) (x+1)^2 - 1 - 1 = 0 or
(5) (x+1)^2 = 2
Now take the square root of each side of (5) to get
(6) x + 1 = +/- sqrt(2) or
(7) x = -1 +/- sqrt(2) or
(8) x = {-1+sqrt(2),-1-sqrt(2)}
To check put x = -1-sqrt(2) into (1).
Is ((-1-sqrt(2))^2 + 2*(-1-sqrt(2) - 1 = 0)?
Is ((1-2sqrt(2)+2) - 2 - 2sqrt(2) - 1 = 0)?
Is (1 - 2sqrt(2) +2 -2 - 2sqrt(2) - 1 = 0)?
Is (1 - 1 = 0)?
Is (0 = 0)? Yes
Answer: x = {-1+sqrt(2),-1-sqrt(2)}
PS you get (7) using the quadratic equation. In fact, completing the square is how the quadratic equation is derived!!!
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