4a^2-56a-16=0

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Solution for 4a^2-56a-16=0 equation: 


Simplifying
4a2 + -56a + -16 = 0

Reorder the terms:
-16 + -56a + 4a2 = 0

Solving
-16 + -56a + 4a2 = 0

Solving for variable 'a'.

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-4 + -14a + a2)' equal to zero and attempt to solve:

Simplifying
-4 + -14a + a2 = 0

Solving
-4 + -14a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -14a + 4 + a2 = 0 + 4

Reorder the terms:
-4 + 4 + -14a + a2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -14a + a2 = 0 + 4
-14a + a2 = 0 + 4

Combine like terms: 0 + 4 = 4
-14a + a2 = 4

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 = 4 + 49

Reorder the terms:
49 + -14a + a2 = 4 + 49

Combine like terms: 4 + 49 = 53
49 + -14a + a2 = 53

Factor a perfect square on the left side:
(a + -7)(a + -7) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(a + -7) equal to 7.280109889 and -7.280109889.


Subproblem 1
a + -7 = 7.280109889

Simplifying
a + -7 = 7.280109889

Reorder the terms:
-7 + a = 7.280109889

Solving
-7 + a = 7.280109889

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 = 7.280109889 + 7

Combine like terms: -7 + 7 = 0
0 + a = 7.280109889 + 7
a = 7.280109889 + 7

Combine like terms: 7.280109889 + 7 = 14.280109889
a = 14.280109889

Simplifying
a = 14.280109889


Subproblem 2
a + -7 = -7.280109889

Simplifying
a + -7 = -7.280109889

Reorder the terms:
-7 + a = -7.280109889

Solving
-7 + a = -7.280109889

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 = -7.280109889 + 7

Combine like terms: -7 + 7 = 0
0 + a = -7.280109889 + 7
a = -7.280109889 + 7

Combine like terms: -7.280109889 + 7 = -0.280109889
a = -0.280109889

Simplifying
a = -0.280109889


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {14.280109889, -0.280109889}
Solution
a = {14.280109889, -0.280109889}

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