4a^2-56a-64=0

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Solution for 4a^2-56a-64=0 equation: 


Simplifying
4a2 + -56a + -64 = 0

Reorder the terms:
-64 + -56a + 4a2 = 0

Solving
-64 + -56a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -14a + a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -14a + a2)' equal to zero and attempt to solve:

Simplifying
-16 + -14a + a2 = 0

Solving
-16 + -14a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -14a + 16 + a2 = 0 + 16

Reorder the terms:
-16 + 16 + -14a + a2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -14a + a2 = 0 + 16
-14a + a2 = 0 + 16

Combine like terms: 0 + 16 = 16
-14a + a2 = 16

The a term is -14a.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14a + 49 + a2 = 16 + 49

Reorder the terms:
49 + -14a + a2 = 16 + 49

Combine like terms: 16 + 49 = 65
49 + -14a + a2 = 65

Factor a perfect square on the left side:
(a + -7)(a + -7) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(a + -7) equal to 8.062257748 and -8.062257748.


Subproblem 1
a + -7 = 8.062257748

Simplifying
a + -7 = 8.062257748

Reorder the terms:
-7 + a = 8.062257748

Solving
-7 + a = 8.062257748

Solving for variable 'a'.

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

Add '7' to each side of the equation.
-7 + 7 + a = 8.062257748 + 7

Combine like terms: -7 + 7 = 0
0 + a = 8.062257748 + 7
a = 8.062257748 + 7

Combine like terms: 8.062257748 + 7 = 15.062257748
a = 15.062257748

Simplifying
a = 15.062257748


Subproblem 2
a + -7 = -8.062257748

Simplifying
a + -7 = -8.062257748

Reorder the terms:
-7 + a = -8.062257748

Solving
-7 + a = -8.062257748

Solving for variable 'a'.

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

Add '7' to each side of the equation.
-7 + 7 + a = -8.062257748 + 7

Combine like terms: -7 + 7 = 0
0 + a = -8.062257748 + 7
a = -8.062257748 + 7

Combine like terms: -8.062257748 + 7 = -1.062257748
a = -1.062257748

Simplifying
a = -1.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {15.062257748, -1.062257748}
Solution
a = {15.062257748, -1.062257748}

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