a^2-10a-80=0

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Solution for a^2-10a-80=0 equation: 


Simplifying
a2 + -10a + -80 = 0

Reorder the terms:
-80 + -10a + a2 = 0

Solving
-80 + -10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -10a + 80 + a2 = 0 + 80

Reorder the terms:
-80 + 80 + -10a + a2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -10a + a2 = 0 + 80
-10a + a2 = 0 + 80

Combine like terms: 0 + 80 = 80
-10a + a2 = 80

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = 80 + 25

Reorder the terms:
25 + -10a + a2 = 80 + 25

Combine like terms: 80 + 25 = 105
25 + -10a + a2 = 105

Factor a perfect square on the left side:
(a + -5)(a + -5) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(a + -5) equal to 10.246950766 and -10.246950766.


Subproblem 1
a + -5 = 10.246950766

Simplifying
a + -5 = 10.246950766

Reorder the terms:
-5 + a = 10.246950766

Solving
-5 + a = 10.246950766

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = 10.246950766 + 5

Combine like terms: -5 + 5 = 0
0 + a = 10.246950766 + 5
a = 10.246950766 + 5

Combine like terms: 10.246950766 + 5 = 15.246950766
a = 15.246950766

Simplifying
a = 15.246950766


Subproblem 2
a + -5 = -10.246950766

Simplifying
a + -5 = -10.246950766

Reorder the terms:
-5 + a = -10.246950766

Solving
-5 + a = -10.246950766

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = -10.246950766 + 5

Combine like terms: -5 + 5 = 0
0 + a = -10.246950766 + 5
a = -10.246950766 + 5

Combine like terms: -10.246950766 + 5 = -5.246950766
a = -5.246950766

Simplifying
a = -5.246950766


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {15.246950766, -5.246950766}

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