-10X^2-40X-4=0

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Solution for -10X^2-40X-4=0 equation: 


Simplifying
-10X2 + -40X + -4 = 0

Reorder the terms:
-4 + -40X + -10X2 = 0

Solving
-4 + -40X + -10X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(2 + 20X + 5X2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(2 + 20X + 5X2)' equal to zero and attempt to solve:

Simplifying
2 + 20X + 5X2 = 0

Solving
2 + 20X + 5X2 = 0

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

Divide each side by '5'.
0.4 + 4X + X2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 4X + -0.4 + X2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 4X + X2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 4X + X2 = 0 + -0.4
4X + X2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
4X + X2 = -0.4

The X term is 4X.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4X + 4 + X2 = -0.4 + 4

Reorder the terms:
4 + 4X + X2 = -0.4 + 4

Combine like terms: -0.4 + 4 = 3.6
4 + 4X + X2 = 3.6

Factor a perfect square on the left side:
(X + 2)(X + 2) = 3.6

Calculate the square root of the right side: 1.897366596

Break this problem into two subproblems by setting 
(X + 2) equal to 1.897366596 and -1.897366596.


Subproblem 1
X + 2 = 1.897366596

Simplifying
X + 2 = 1.897366596

Reorder the terms:
2 + X = 1.897366596

Solving
2 + X = 1.897366596

Solving for variable 'X'.

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

Add '-2' to each side of the equation.
2 + -2 + X = 1.897366596 + -2

Combine like terms: 2 + -2 = 0
0 + X = 1.897366596 + -2
X = 1.897366596 + -2

Combine like terms: 1.897366596 + -2 = -0.102633404
X = -0.102633404

Simplifying
X = -0.102633404


Subproblem 2
X + 2 = -1.897366596

Simplifying
X + 2 = -1.897366596

Reorder the terms:
2 + X = -1.897366596

Solving
2 + X = -1.897366596

Solving for variable 'X'.

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

Add '-2' to each side of the equation.
2 + -2 + X = -1.897366596 + -2

Combine like terms: 2 + -2 = 0
0 + X = -1.897366596 + -2
X = -1.897366596 + -2

Combine like terms: -1.897366596 + -2 = -3.897366596
X = -3.897366596

Simplifying
X = -3.897366596


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.102633404, -3.897366596}
Solution
X = {-0.102633404, -3.897366596}

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