a^2-4a-32=32

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Solution for a^2-4a-32=32 equation: 


Simplifying
a2 + -4a + -32 = 32

Reorder the terms:
-32 + -4a + a2 = 32

Solving
-32 + -4a + a2 = 32

Solving for variable 'a'.

Reorder the terms:
-32 + -32 + -4a + a2 = 32 + -32

Combine like terms: -32 + -32 = -64
-64 + -4a + a2 = 32 + -32

Combine like terms: 32 + -32 = 0
-64 + -4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -4a + 64 + a2 = 0 + 64

Reorder the terms:
-64 + 64 + -4a + a2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -4a + a2 = 0 + 64
-4a + a2 = 0 + 64

Combine like terms: 0 + 64 = 64
-4a + a2 = 64

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = 64 + 4

Reorder the terms:
4 + -4a + a2 = 64 + 4

Combine like terms: 64 + 4 = 68
4 + -4a + a2 = 68

Factor a perfect square on the left side:
(a + -2)(a + -2) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(a + -2) equal to 8.246211251 and -8.246211251.


Subproblem 1
a + -2 = 8.246211251

Simplifying
a + -2 = 8.246211251

Reorder the terms:
-2 + a = 8.246211251

Solving
-2 + a = 8.246211251

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = 8.246211251 + 2

Combine like terms: -2 + 2 = 0
0 + a = 8.246211251 + 2
a = 8.246211251 + 2

Combine like terms: 8.246211251 + 2 = 10.246211251
a = 10.246211251

Simplifying
a = 10.246211251


Subproblem 2
a + -2 = -8.246211251

Simplifying
a + -2 = -8.246211251

Reorder the terms:
-2 + a = -8.246211251

Solving
-2 + a = -8.246211251

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = -8.246211251 + 2

Combine like terms: -2 + 2 = 0
0 + a = -8.246211251 + 2
a = -8.246211251 + 2

Combine like terms: -8.246211251 + 2 = -6.246211251
a = -6.246211251

Simplifying
a = -6.246211251


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {10.246211251, -6.246211251}

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