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

Jul 21, 2015

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

Explanation:

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

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

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

${x}^{2} + 2 \cdot x \cdot 2 + {2}^{2} = 5$

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

$x + 2 = \sqrt{5}$ or $x + 2 = - \sqrt{5}$

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