a^2-12a-43=0

Solution for a^2-12a-43=0 equation:

Simplifying
a2 + -12a + -43 = 0

Reorder the terms:
-43 + -12a + a2 = 0

Solving
-43 + -12a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -12a + 43 + a2 = 0 + 43

Reorder the terms:
-43 + 43 + -12a + a2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -12a + a2 = 0 + 43
-12a + a2 = 0 + 43

Combine like terms: 0 + 43 = 43
-12a + a2 = 43

The a term is -12a.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12a + 36 + a2 = 43 + 36

Reorder the terms:
36 + -12a + a2 = 43 + 36

Combine like terms: 43 + 36 = 79
36 + -12a + a2 = 79

Factor a perfect square on the left side:
(a + -6)(a + -6) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(a + -6) equal to 8.888194417 and -8.888194417.

Subproblem 1
a + -6 = 8.888194417

Simplifying
a + -6 = 8.888194417

Reorder the terms:
-6 + a = 8.888194417

Solving
-6 + a = 8.888194417

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a = 8.888194417 + 6

Combine like terms: -6 + 6 = 0
0 + a = 8.888194417 + 6
a = 8.888194417 + 6

Combine like terms: 8.888194417 + 6 = 14.888194417
a = 14.888194417

Simplifying
a = 14.888194417

Subproblem 2
a + -6 = -8.888194417

Simplifying
a + -6 = -8.888194417

Reorder the terms:
-6 + a = -8.888194417

Solving
-6 + a = -8.888194417

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a = -8.888194417 + 6

Combine like terms: -6 + 6 = 0
0 + a = -8.888194417 + 6
a = -8.888194417 + 6

Combine like terms: -8.888194417 + 6 = -2.888194417
a = -2.888194417

Simplifying
a = -2.888194417

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {14.888194417, -2.888194417}