How do you solve the quadratic equation by completing the square: $x^2+4x-1=0$ ?

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Answer 1 · 2015-07-21T16:28:47

$color(green)(x = sqrt 5 - 2$ or $color(green)(x = -sqrt 5-2$

$x^2 + 4x = 1$

To write the left hand side as a perfect square, we add 4 to both sides:

$x^2 + 4x + 4= 1 + 4$

$x^2 + 2*x*2 + 2^2 = 5$

Using the Identity $color(blue)((a+b)^2 = a^2 + 2ab + b^2$ , we get
$(x+2)^2 = 5$

$x + 2 = sqrt5$ or $x +2 = -sqrt5$

$color(green)(x = sqrt 5 - 2$ or $color(green)(x = -sqrt 5-2$

How do you solve the quadratic equation by completing the square: x^2+4x-1=0x^2+4x-1=0?