6+a-4-3a^2-a^2-5a=

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Solution for 6+a-4-3a^2-a^2-5a= equation: 


Simplifying
6 + a + -4 + -3a2 + -1a2 + -5a = 0

Reorder the terms:
6 + -4 + a + -5a + -3a2 + -1a2 = 0

Combine like terms: 6 + -4 = 2
2 + a + -5a + -3a2 + -1a2 = 0

Combine like terms: a + -5a = -4a
2 + -4a + -3a2 + -1a2 = 0

Combine like terms: -3a2 + -1a2 = -4a2
2 + -4a + -4a2 = 0

Solving
2 + -4a + -4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2a + -2a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -2a + -2a2)' equal to zero and attempt to solve:

Simplifying
1 + -2a + -2a2 = 0

Solving
1 + -2a + -2a2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-0.5 + a + a2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a + a2 = 0 + 0.5
a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
a + a2 = 0.5

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + a2 = 0.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + a2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
1.25 + a2 = 0.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.866025404 and -0.866025404.


Subproblem 1
a + 0.5 = 0.866025404

Simplifying
a + 0.5 = 0.866025404

Reorder the terms:
0.5 + a = 0.866025404

Solving
0.5 + a = 0.866025404

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 0.866025404 + -0.5
a = 0.866025404 + -0.5

Combine like terms: 0.866025404 + -0.5 = 0.366025404
a = 0.366025404

Simplifying
a = 0.366025404


Subproblem 2
a + 0.5 = -0.866025404

Simplifying
a + 0.5 = -0.866025404

Reorder the terms:
0.5 + a = -0.866025404

Solving
0.5 + a = -0.866025404

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -0.866025404 + -0.5
a = -0.866025404 + -0.5

Combine like terms: -0.866025404 + -0.5 = -1.366025404
a = -1.366025404

Simplifying
a = -1.366025404


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.366025404, -1.366025404}
Solution
a = {0.366025404, -1.366025404}

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