Question

Solve the equation: x^2+4x+1=0

Answer 1

An equation in the form: \[ax^2+bx+c=0\] has solutions: \[x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]
just compare coefficients, substitute into the formula and your answers should fall out :-)

Answer 2

this is correct but you can also use the "completing the square" method which in this case is simpler

Answer 3

Does the answer end up as: x=-2(+or-) 2√3?

Answer 4

\[x=\frac{ -4 \pm \sqrt{4^2-4*1*1} }{ 2}=\frac{ -4 \pm \sqrt{12} }{ 2 }=\frac{ -4 \pm 2\sqrt{3} }{ 2 }=-2 \pm \sqrt{3}\]

yep you're right :-)

Answer 5

oh wait it's root 3 not 2root3

Answer 6

Does it get rid of that 2 that goes before the √3 because 2/2=1 so it turns into: -2(+or-)√3?

Answer 7

exactly! both the -4 and the 2root3 cancel with the 2 at the bottom :-)
and obviously -4/2=-2 (which you got) and 2root3/2=root3

Answer 8

Ok thank you! I see where it all comes from now.

Answer 9

you're very welcome :-)