15a^2-16a-4=0

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Solution for 15a^2-16a-4=0 equation: 


Simplifying
15a2 + -16a + -4 = 0

Reorder the terms:
-4 + -16a + 15a2 = 0

Solving
-4 + -16a + 15a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
-0.2666666667 + -1.066666667a + a2 = 0

Move the constant term to the right:

Add '0.2666666667' to each side of the equation.
-0.2666666667 + -1.066666667a + 0.2666666667 + a2 = 0 + 0.2666666667

Reorder the terms:
-0.2666666667 + 0.2666666667 + -1.066666667a + a2 = 0 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + -1.066666667a + a2 = 0 + 0.2666666667
-1.066666667a + a2 = 0 + 0.2666666667

Combine like terms: 0 + 0.2666666667 = 0.2666666667
-1.066666667a + a2 = 0.2666666667

The a term is -1.066666667a.  Take half its coefficient (-0.5333333335).
Square it (0.2844444446) and add it to both sides.

Add '0.2844444446' to each side of the equation.
-1.066666667a + 0.2844444446 + a2 = 0.2666666667 + 0.2844444446

Reorder the terms:
0.2844444446 + -1.066666667a + a2 = 0.2666666667 + 0.2844444446

Combine like terms: 0.2666666667 + 0.2844444446 = 0.5511111113
0.2844444446 + -1.066666667a + a2 = 0.5511111113

Factor a perfect square on the left side:
(a + -0.5333333335)(a + -0.5333333335) = 0.5511111113

Calculate the square root of the right side: 0.742368582

Break this problem into two subproblems by setting 
(a + -0.5333333335) equal to 0.742368582 and -0.742368582.


Subproblem 1
a + -0.5333333335 = 0.742368582

Simplifying
a + -0.5333333335 = 0.742368582

Reorder the terms:
-0.5333333335 + a = 0.742368582

Solving
-0.5333333335 + a = 0.742368582

Solving for variable 'a'.

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

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + a = 0.742368582 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + a = 0.742368582 + 0.5333333335
a = 0.742368582 + 0.5333333335

Combine like terms: 0.742368582 + 0.5333333335 = 1.2757019155
a = 1.2757019155

Simplifying
a = 1.2757019155


Subproblem 2
a + -0.5333333335 = -0.742368582

Simplifying
a + -0.5333333335 = -0.742368582

Reorder the terms:
-0.5333333335 + a = -0.742368582

Solving
-0.5333333335 + a = -0.742368582

Solving for variable 'a'.

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

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + a = -0.742368582 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + a = -0.742368582 + 0.5333333335
a = -0.742368582 + 0.5333333335

Combine like terms: -0.742368582 + 0.5333333335 = -0.2090352485
a = -0.2090352485

Simplifying
a = -0.2090352485


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.2757019155, -0.2090352485}

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