a^2-20a+44=0

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Solution for a^2-20a+44=0 equation: 


Simplifying
a2 + -20a + 44 = 0

Reorder the terms:
44 + -20a + a2 = 0

Solving
44 + -20a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + -20a + -44 + a2 = 0 + -44

Reorder the terms:
44 + -44 + -20a + a2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -20a + a2 = 0 + -44
-20a + a2 = 0 + -44

Combine like terms: 0 + -44 = -44
-20a + a2 = -44

The a term is -20a.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20a + 100 + a2 = -44 + 100

Reorder the terms:
100 + -20a + a2 = -44 + 100

Combine like terms: -44 + 100 = 56
100 + -20a + a2 = 56

Factor a perfect square on the left side:
(a + -10)(a + -10) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(a + -10) equal to 7.483314774 and -7.483314774.


Subproblem 1
a + -10 = 7.483314774

Simplifying
a + -10 = 7.483314774

Reorder the terms:
-10 + a = 7.483314774

Solving
-10 + a = 7.483314774

Solving for variable 'a'.

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

Add '10' to each side of the equation.
-10 + 10 + a = 7.483314774 + 10

Combine like terms: -10 + 10 = 0
0 + a = 7.483314774 + 10
a = 7.483314774 + 10

Combine like terms: 7.483314774 + 10 = 17.483314774
a = 17.483314774

Simplifying
a = 17.483314774


Subproblem 2
a + -10 = -7.483314774

Simplifying
a + -10 = -7.483314774

Reorder the terms:
-10 + a = -7.483314774

Solving
-10 + a = -7.483314774

Solving for variable 'a'.

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

Add '10' to each side of the equation.
-10 + 10 + a = -7.483314774 + 10

Combine like terms: -10 + 10 = 0
0 + a = -7.483314774 + 10
a = -7.483314774 + 10

Combine like terms: -7.483314774 + 10 = 2.516685226
a = 2.516685226

Simplifying
a = 2.516685226


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {17.483314774, 2.516685226}

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