Question

How do i rewrite the equation?

Answer 1

Answer+Step-by-step explanation:

1)

$x^{2}+4x+1=x^{2}+4x + (4 - 4) + 1$

                  $=x^{2}+4x + 4 - 3$

                  $=(x+2)^2-3$

then

$x^{2}+4x+1=0$

$\Longleftrightarrow \left( x+2\right)^{2} -3=0$

$\Longleftrightarrow \left( x+2\right)^{2} =3$

2)

$\left( x+2\right)^{2} =3$

⇔ |x + 2| = √3

⇔ x + 2 = √3 or x + 2 = -√3

⇔ x + 2 = ±√3

⇔ x = -2 ± √3