Two solutions were found :
 x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i
 x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i
Step by step solution :
Step  1  :
Equation at the end of step  1  :
  ((0 -  5x2) -  4x) -  4  = 0 
Step  2  :
Step  3  :
Pulling out like terms :
 3.1     Pull out like factors :
   -5x2 - 4x - 4  =   -1 • (5x2 + 4x + 4) 
Trying to factor by splitting the middle term
 3.2     Factoring  5x2 + 4x + 4 
The first term is,  5x2  its coefficient is  5 .
The middle term is,  +4x  its coefficient is  4 .
The last term, "the constant", is  +4 
Step-1 : Multiply the coefficient of the first term by the constant   5 • 4 = 20 
Step-2 : Find two factors of  20  whose sum equals the coefficient of the middle term, which is   4 .
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step  3  :
  -5x2 - 4x - 4  = 0 
Step  4  :
Parabola, Finding the Vertex :
 4.1      Find the Vertex of   y = -5x2-4x-4
 For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.4000  
 Plugging into the parabola formula  -0.4000  for  x  we can calculate the  y -coordinate : 
  y = -5.0 * -0.40 * -0.40 - 4.0 * -0.40 - 4.0
or   y = -3.200
Parabola, Graphing Vertex and X-Intercepts :
Root plot for :  y = -5x2-4x-4
Axis of Symmetry (dashed)  {x}={-0.40} 
Vertex at  {x,y} = {-0.40,-3.20} 
Function has no real roots
Solve Quadratic Equation by Completing The Square
 4.2     Solving   -5x2-4x-4 = 0 by Completing The Square .
 Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:
 5x2+4x+4 = 0  Divide both sides of the equation by  5  to have 1 as the coefficient of the first term :
   x2+(4/5)x+(4/5) = 0
Subtract  4/5  from both side of the equation :
   x2+(4/5)x = -4/5
Add  4/25  to both sides of the equation :
  On the right hand side we have :
   -4/5  +  4/25   The common denominator of the two fractions is  25   Adding  (-20/25)+(4/25)  gives  -16/25 
  So adding to both sides we finally get :
   x2+(4/5)x+(4/25) = -16/25
Adding  4/25  has completed the left hand side into a perfect square :
   x2+(4/5)x+(4/25)  =
   (x+(2/5)) • (x+(2/5))  =
  (x+(2/5))2
Things which are equal to the same thing are also equal to one another. Since
   x2+(4/5)x+(4/25) = -16/25 and
   x2+(4/5)x+(4/25) = (x+(2/5))2
then, according to the law of transitivity,
   (x+(2/5))2 = -16/25
Note that the square root of
   (x+(2/5))2   is
   (x+(2/5))2/2 =
  (x+(2/5))1 =
   x+(2/5)
Now, applying the Square Root Principle to  Eq. #4.2.1  we get:
   x+(2/5) = √ -16/25
Subtract  2/5  from both sides to obtain:
   x = -2/5 + √ -16/25
Since a square root has two values, one positive and the other negative
   x2 + (4/5)x + (4/5) = 0
   has two solutions:
  x = -2/5 + √ 16/25 •  i 
   or
  x = -2/5 - √ 16/25 •  i 
Note that  √ 16/25 can be written as
  √ 16  / √ 25   which is 4 / 5
Solve Quadratic Equation using the Quadratic Formula
 4.3     Solving    -5x2-4x-4 = 0 by the Quadratic Formula .
 According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :
                                     
            - B  ±  √ B2-4AC
  x =   ————————
                      2A
  In our case,  A   =     -5
                      B   =    -4
                      C   =   -4
Accordingly,  B2  -  4AC   =
                     16 - 80 =
                     -64
Applying the quadratic formula :
               4 ± √ -64
   x  =    —————
                    -10
In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i) 
Both   i   and   -i   are the square roots of minus 1
Accordingly,√ -64  = 
                    √ 64 • (-1)  =
                    √ 64  • √ -1   =
                    ±  √ 64  • i
Can  √ 64 be simplified ?
Yes!   The prime factorization of  64   is
   2•2•2•2•2•2 
To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).
√ 64   =  √ 2•2•2•2•2•2   =2•2•2•√ 1   =
                ±  8 • √ 1   =
                ±  8
So now we are looking at:
           x  =  ( 4 ± 8i ) / -10
Two imaginary solutions :
 x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i
  or: 
 x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i
Two solutions were found :
 x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i
 x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i
<em>hope i helped</em>
<em>-Rin:)</em>