a^2-16.38a-45.86=0

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Solution for a^2-16.38a-45.86=0 equation: 


Simplifying
a2 + -16.38a + -45.86 = 0

Reorder the terms:
-45.86 + -16.38a + a2 = 0

Solving
-45.86 + -16.38a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '45.86' to each side of the equation.
-45.86 + -16.38a + 45.86 + a2 = 0 + 45.86

Reorder the terms:
-45.86 + 45.86 + -16.38a + a2 = 0 + 45.86

Combine like terms: -45.86 + 45.86 = 0.00
0.00 + -16.38a + a2 = 0 + 45.86
-16.38a + a2 = 0 + 45.86

Combine like terms: 0 + 45.86 = 45.86
-16.38a + a2 = 45.86

The a term is -16.38a.  Take half its coefficient (-8.19).
Square it (67.0761) and add it to both sides.

Add '67.0761' to each side of the equation.
-16.38a + 67.0761 + a2 = 45.86 + 67.0761

Reorder the terms:
67.0761 + -16.38a + a2 = 45.86 + 67.0761

Combine like terms: 45.86 + 67.0761 = 112.9361
67.0761 + -16.38a + a2 = 112.9361

Factor a perfect square on the left side:
(a + -8.19)(a + -8.19) = 112.9361

Calculate the square root of the right side: 10.627139785

Break this problem into two subproblems by setting 
(a + -8.19) equal to 10.627139785 and -10.627139785.


Subproblem 1
a + -8.19 = 10.627139785

Simplifying
a + -8.19 = 10.627139785

Reorder the terms:
-8.19 + a = 10.627139785

Solving
-8.19 + a = 10.627139785

Solving for variable 'a'.

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

Add '8.19' to each side of the equation.
-8.19 + 8.19 + a = 10.627139785 + 8.19

Combine like terms: -8.19 + 8.19 = 0.00
0.00 + a = 10.627139785 + 8.19
a = 10.627139785 + 8.19

Combine like terms: 10.627139785 + 8.19 = 18.817139785
a = 18.817139785

Simplifying
a = 18.817139785


Subproblem 2
a + -8.19 = -10.627139785

Simplifying
a + -8.19 = -10.627139785

Reorder the terms:
-8.19 + a = -10.627139785

Solving
-8.19 + a = -10.627139785

Solving for variable 'a'.

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

Add '8.19' to each side of the equation.
-8.19 + 8.19 + a = -10.627139785 + 8.19

Combine like terms: -8.19 + 8.19 = 0.00
0.00 + a = -10.627139785 + 8.19
a = -10.627139785 + 8.19

Combine like terms: -10.627139785 + 8.19 = -2.437139785
a = -2.437139785

Simplifying
a = -2.437139785


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {18.817139785, -2.437139785}

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