a^2-16a-5=0

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Solution for a^2-16a-5=0 equation: 


Simplifying
a2 + -16a + -5 = 0

Reorder the terms:
-5 + -16a + a2 = 0

Solving
-5 + -16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -16a + 5 + a2 = 0 + 5

Reorder the terms:
-5 + 5 + -16a + a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -16a + a2 = 0 + 5
-16a + a2 = 0 + 5

Combine like terms: 0 + 5 = 5
-16a + a2 = 5

The a term is -16a.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16a + 64 + a2 = 5 + 64

Reorder the terms:
64 + -16a + a2 = 5 + 64

Combine like terms: 5 + 64 = 69
64 + -16a + a2 = 69

Factor a perfect square on the left side:
(a + -8)(a + -8) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(a + -8) equal to 8.306623863 and -8.306623863.


Subproblem 1
a + -8 = 8.306623863

Simplifying
a + -8 = 8.306623863

Reorder the terms:
-8 + a = 8.306623863

Solving
-8 + a = 8.306623863

Solving for variable 'a'.

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

Add '8' to each side of the equation.
-8 + 8 + a = 8.306623863 + 8

Combine like terms: -8 + 8 = 0
0 + a = 8.306623863 + 8
a = 8.306623863 + 8

Combine like terms: 8.306623863 + 8 = 16.306623863
a = 16.306623863

Simplifying
a = 16.306623863


Subproblem 2
a + -8 = -8.306623863

Simplifying
a + -8 = -8.306623863

Reorder the terms:
-8 + a = -8.306623863

Solving
-8 + a = -8.306623863

Solving for variable 'a'.

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

Add '8' to each side of the equation.
-8 + 8 + a = -8.306623863 + 8

Combine like terms: -8 + 8 = 0
0 + a = -8.306623863 + 8
a = -8.306623863 + 8

Combine like terms: -8.306623863 + 8 = -0.306623863
a = -0.306623863

Simplifying
a = -0.306623863


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {16.306623863, -0.306623863}

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