a^2-16a-12=0

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Solution for a^2-16a-12=0 equation: 


Simplifying
a2 + -16a + -12 = 0

Reorder the terms:
-12 + -16a + a2 = 0

Solving
-12 + -16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -16a + 12 + a2 = 0 + 12

Reorder the terms:
-12 + 12 + -16a + a2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -16a + a2 = 0 + 12
-16a + a2 = 0 + 12

Combine like terms: 0 + 12 = 12
-16a + a2 = 12

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 = 12 + 64

Reorder the terms:
64 + -16a + a2 = 12 + 64

Combine like terms: 12 + 64 = 76
64 + -16a + a2 = 76

Factor a perfect square on the left side:
(a + -8)(a + -8) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(a + -8) equal to 8.717797887 and -8.717797887.


Subproblem 1
a + -8 = 8.717797887

Simplifying
a + -8 = 8.717797887

Reorder the terms:
-8 + a = 8.717797887

Solving
-8 + a = 8.717797887

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 = 8.717797887 + 8

Combine like terms: -8 + 8 = 0
0 + a = 8.717797887 + 8
a = 8.717797887 + 8

Combine like terms: 8.717797887 + 8 = 16.717797887
a = 16.717797887

Simplifying
a = 16.717797887


Subproblem 2
a + -8 = -8.717797887

Simplifying
a + -8 = -8.717797887

Reorder the terms:
-8 + a = -8.717797887

Solving
-8 + a = -8.717797887

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 = -8.717797887 + 8

Combine like terms: -8 + 8 = 0
0 + a = -8.717797887 + 8
a = -8.717797887 + 8

Combine like terms: -8.717797887 + 8 = -0.717797887
a = -0.717797887

Simplifying
a = -0.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {16.717797887, -0.717797887}

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