a^2-16a-32=0

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Solution for a^2-16a-32=0 equation: 


Simplifying
a2 + -16a + -32 = 0

Reorder the terms:
-32 + -16a + a2 = 0

Solving
-32 + -16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -16a + 32 + a2 = 0 + 32

Reorder the terms:
-32 + 32 + -16a + a2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -16a + a2 = 0 + 32
-16a + a2 = 0 + 32

Combine like terms: 0 + 32 = 32
-16a + a2 = 32

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 = 32 + 64

Reorder the terms:
64 + -16a + a2 = 32 + 64

Combine like terms: 32 + 64 = 96
64 + -16a + a2 = 96

Factor a perfect square on the left side:
(a + -8)(a + -8) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(a + -8) equal to 9.797958971 and -9.797958971.


Subproblem 1
a + -8 = 9.797958971

Simplifying
a + -8 = 9.797958971

Reorder the terms:
-8 + a = 9.797958971

Solving
-8 + a = 9.797958971

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 = 9.797958971 + 8

Combine like terms: -8 + 8 = 0
0 + a = 9.797958971 + 8
a = 9.797958971 + 8

Combine like terms: 9.797958971 + 8 = 17.797958971
a = 17.797958971

Simplifying
a = 17.797958971


Subproblem 2
a + -8 = -9.797958971

Simplifying
a + -8 = -9.797958971

Reorder the terms:
-8 + a = -9.797958971

Solving
-8 + a = -9.797958971

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 = -9.797958971 + 8

Combine like terms: -8 + 8 = 0
0 + a = -9.797958971 + 8
a = -9.797958971 + 8

Combine like terms: -9.797958971 + 8 = -1.797958971
a = -1.797958971

Simplifying
a = -1.797958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {17.797958971, -1.797958971}

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