12a^2-6a-5=0

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Solution for 12a^2-6a-5=0 equation:


Simplifying
12a2 + -6a + -5 = 0

Reorder the terms:
-5 + -6a + 12a2 = 0

Solving
-5 + -6a + 12a2 = 0

Solving for variable 'a'.

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

Divide each side by '12'.
-0.4166666667 + -0.5a + a2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -0.5a + 0.4166666667 + a2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -0.5a + a2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -0.5a + a2 = 0 + 0.4166666667
-0.5a + a2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-0.5a + a2 = 0.4166666667

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = 0.4166666667 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = 0.4166666667 + 0.0625

Combine like terms: 0.4166666667 + 0.0625 = 0.4791666667
0.0625 + -0.5a + a2 = 0.4791666667

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = 0.4791666667

Calculate the square root of the right side: 0.692218655

Break this problem into two subproblems by setting 
(a + -0.25) equal to 0.692218655 and -0.692218655.

Subproblem 1

a + -0.25 = 0.692218655 Simplifying a + -0.25 = 0.692218655 Reorder the terms: -0.25 + a = 0.692218655 Solving -0.25 + a = 0.692218655 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 0.692218655 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 0.692218655 + 0.25 a = 0.692218655 + 0.25 Combine like terms: 0.692218655 + 0.25 = 0.942218655 a = 0.942218655 Simplifying a = 0.942218655

Subproblem 2

a + -0.25 = -0.692218655 Simplifying a + -0.25 = -0.692218655 Reorder the terms: -0.25 + a = -0.692218655 Solving -0.25 + a = -0.692218655 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -0.692218655 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -0.692218655 + 0.25 a = -0.692218655 + 0.25 Combine like terms: -0.692218655 + 0.25 = -0.442218655 a = -0.442218655 Simplifying a = -0.442218655

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.942218655, -0.442218655}

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