-4a^2+36a+80=0

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Solution for -4a^2+36a+80=0 equation: 


Simplifying
-4a2 + 36a + 80 = 0

Reorder the terms:
80 + 36a + -4a2 = 0

Solving
80 + 36a + -4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + 9a + -1a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + 9a + -1a2)' equal to zero and attempt to solve:

Simplifying
20 + 9a + -1a2 = 0

Solving
20 + 9a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-20 + -9a + a2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -9a + 20 + a2 = 0 + 20

Reorder the terms:
-20 + 20 + -9a + a2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -9a + a2 = 0 + 20
-9a + a2 = 0 + 20

Combine like terms: 0 + 20 = 20
-9a + a2 = 20

The a term is -9a.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9a + 20.25 + a2 = 20 + 20.25

Reorder the terms:
20.25 + -9a + a2 = 20 + 20.25

Combine like terms: 20 + 20.25 = 40.25
20.25 + -9a + a2 = 40.25

Factor a perfect square on the left side:
(a + -4.5)(a + -4.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(a + -4.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
a + -4.5 = 6.34428877

Simplifying
a + -4.5 = 6.34428877

Reorder the terms:
-4.5 + a = 6.34428877

Solving
-4.5 + a = 6.34428877

Solving for variable 'a'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + a = 6.34428877 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + a = 6.34428877 + 4.5
a = 6.34428877 + 4.5

Combine like terms: 6.34428877 + 4.5 = 10.84428877
a = 10.84428877

Simplifying
a = 10.84428877


Subproblem 2
a + -4.5 = -6.34428877

Simplifying
a + -4.5 = -6.34428877

Reorder the terms:
-4.5 + a = -6.34428877

Solving
-4.5 + a = -6.34428877

Solving for variable 'a'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + a = -6.34428877 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + a = -6.34428877 + 4.5
a = -6.34428877 + 4.5

Combine like terms: -6.34428877 + 4.5 = -1.84428877
a = -1.84428877

Simplifying
a = -1.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {10.84428877, -1.84428877}
Solution
a = {10.84428877, -1.84428877}

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