Question

How do you solve `x^2 + 4x + 1 = 0` using the quadratic formula?

Answer 1

`x=-2+-sqrt3`

Explanation:

`"Given the quadratic equation in standard form"`

`•color(white)(x)ax^2+bx+c=0 color(white)(x);a!=0`

`"We can solve for x using the "color(blue)"quadratic formula"`

`•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)`

`x^2+4x+1=0" is in standard form"`

`"with "a=1,b=4" and "c=1`

`rArrx=(-4+-sqrt(16-4))/2=(-4+-sqrt12)/2`

`color(white)(x)=(-4+-2sqrt3)/2=-2+-sqrt3larrcolor(red)"exact values"`