4a(a-13)=80

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Solution for 4a(a-13)=80 equation: 


Simplifying
4a(a + -13) = 80

Reorder the terms:
4a(-13 + a) = 80
(-13 * 4a + a * 4a) = 80
(-52a + 4a2) = 80

Solving
-52a + 4a2 = 80

Solving for variable 'a'.

Reorder the terms:
-80 + -52a + 4a2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + -52a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + -13a + a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + -13a + a2)' equal to zero and attempt to solve:

Simplifying
-20 + -13a + a2 = 0

Solving
-20 + -13a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -13a + 20 + a2 = 0 + 20

Reorder the terms:
-20 + 20 + -13a + a2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -13a + a2 = 0 + 20
-13a + a2 = 0 + 20

Combine like terms: 0 + 20 = 20
-13a + a2 = 20

The a term is -13a.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13a + 42.25 + a2 = 20 + 42.25

Reorder the terms:
42.25 + -13a + a2 = 20 + 42.25

Combine like terms: 20 + 42.25 = 62.25
42.25 + -13a + a2 = 62.25

Factor a perfect square on the left side:
(a + -6.5)(a + -6.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(a + -6.5) equal to 7.889866919 and -7.889866919.


Subproblem 1
a + -6.5 = 7.889866919

Simplifying
a + -6.5 = 7.889866919

Reorder the terms:
-6.5 + a = 7.889866919

Solving
-6.5 + a = 7.889866919

Solving for variable 'a'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + a = 7.889866919 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + a = 7.889866919 + 6.5
a = 7.889866919 + 6.5

Combine like terms: 7.889866919 + 6.5 = 14.389866919
a = 14.389866919

Simplifying
a = 14.389866919


Subproblem 2
a + -6.5 = -7.889866919

Simplifying
a + -6.5 = -7.889866919

Reorder the terms:
-6.5 + a = -7.889866919

Solving
-6.5 + a = -7.889866919

Solving for variable 'a'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + a = -7.889866919 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + a = -7.889866919 + 6.5
a = -7.889866919 + 6.5

Combine like terms: -7.889866919 + 6.5 = -1.389866919
a = -1.389866919

Simplifying
a = -1.389866919


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {14.389866919, -1.389866919}
Solution
a = {14.389866919, -1.389866919}

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