Quadratic Formula?

Question

2x^2 + 4x = -1

I have this problem most of the way done, I am just stuck now...wondering if you could help...

2x^2+4x+1=0

-4+/- SQRT[(4)^2 - 4(2)(1)] / 2 (2)

-4 +/- SQRT (16-8) / 4
-4 +/- SQRT (8) / 4

so.....
-4 + SQRT 8 / 4 or -4 - SQRT 8 / 4

is that it? Can it be simplified more? Whats the final answer then?

Answer 1

Quadratic Formula

x = - b ± √b² - 4ac / 2a

2x² + 4x = - 1

2x² + 4x + 1 + - 1 + 1

2x² + 4x + 1 = 0

Let

a = 2

b = 4

c = 1

- - - - - - -

x = - 4 ± √(4)² - 4(2)(1) / 2(2)

x = - 4 ± √16 - 8 / 4

x = - 4 ± √8 / 4

x = - 4 ± 2.828427125 / 4

- - - - - - - -

Solving for +

x = - 4 + 2.828427125 / 4

x = - 1.171572875 / 4

x = - 0.292893219

- - - - - - - -

Solving for -

x = - 4 - 2.828427125 / 4

x = - 6.828427125 / 4

x = - 1.707106781

- - - - - - - s-

Answer 2

2x^2+4x+1=0
here a=2,b=4,c=1
the formula is
x=[-b+-sqrt(b^2-4ac)]/2a
so x=[-4+-sqrt(4^2-4.2.1)]/2.2
=[-4+-sqrt(16-8)]/4
=[-4+-sqrt8]/4
=[-4+-2sqrt2]/4
=[-2+-sqrt2]/2
so the roots are [-2+sqrt2]/2 &[-2-sqrt2]/2

Answer 3

another form of eq is :

x^2 + 2x + (1/2) = 0
x = {(-2)(+/-)sqrt(2)}/2
so x= -1 +(1/sqrt2)
or x = -1 -(1/sqrt2)

Answer 4

A bit more...

-1 + 0.5*sqt(2) or
-1 - 0.5*sqt(2)

Answer 5

Sometimes, that's as simple as it gets.