5x^2-4x-4=0

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Solution for 5x^2-4x-4=0 equation: 


Simplifying
5x2 + -4x + -4 = 0

Reorder the terms:
-4 + -4x + 5x2 = 0

Solving
-4 + -4x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.8 + -0.8x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -0.8x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -0.8x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -0.8x + x2 = 0 + 0.8
-0.8x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-0.8x + x2 = 0.8

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 0.8 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 0.8 + 0.16

Combine like terms: 0.8 + 0.16 = 0.96
0.16 + -0.8x + x2 = 0.96

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.979795897 and -0.979795897.


Subproblem 1
x + -0.4 = 0.979795897

Simplifying
x + -0.4 = 0.979795897

Reorder the terms:
-0.4 + x = 0.979795897

Solving
-0.4 + x = 0.979795897

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 0.979795897 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 0.979795897 + 0.4
x = 0.979795897 + 0.4

Combine like terms: 0.979795897 + 0.4 = 1.379795897
x = 1.379795897

Simplifying
x = 1.379795897


Subproblem 2
x + -0.4 = -0.979795897

Simplifying
x + -0.4 = -0.979795897

Reorder the terms:
-0.4 + x = -0.979795897

Solving
-0.4 + x = -0.979795897

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -0.979795897 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -0.979795897 + 0.4
x = -0.979795897 + 0.4

Combine like terms: -0.979795897 + 0.4 = -0.579795897
x = -0.579795897

Simplifying
x = -0.579795897


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.379795897, -0.579795897}

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