12n^2-7n-7=0

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Solution for 12n^2-7n-7=0 equation: 


Simplifying
12n2 + -7n + -7 = 0

Reorder the terms:
-7 + -7n + 12n2 = 0

Solving
-7 + -7n + 12n2 = 0

Solving for variable 'n'.

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

Divide each side by '12'.
-0.5833333333 + -0.5833333333n + n2 = 0

Move the constant term to the right:

Add '0.5833333333' to each side of the equation.
-0.5833333333 + -0.5833333333n + 0.5833333333 + n2 = 0 + 0.5833333333

Reorder the terms:
-0.5833333333 + 0.5833333333 + -0.5833333333n + n2 = 0 + 0.5833333333

Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000
0.0000000000 + -0.5833333333n + n2 = 0 + 0.5833333333
-0.5833333333n + n2 = 0 + 0.5833333333

Combine like terms: 0 + 0.5833333333 = 0.5833333333
-0.5833333333n + n2 = 0.5833333333

The n term is -0.5833333333n.  Take half its coefficient (-0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
-0.5833333333n + 0.08506944446 + n2 = 0.5833333333 + 0.08506944446

Reorder the terms:
0.08506944446 + -0.5833333333n + n2 = 0.5833333333 + 0.08506944446

Combine like terms: 0.5833333333 + 0.08506944446 = 0.66840277776
0.08506944446 + -0.5833333333n + n2 = 0.66840277776

Factor a perfect square on the left side:
(n + -0.2916666667)(n + -0.2916666667) = 0.66840277776

Calculate the square root of the right side: 0.817559036

Break this problem into two subproblems by setting 
(n + -0.2916666667) equal to 0.817559036 and -0.817559036.


Subproblem 1
n + -0.2916666667 = 0.817559036

Simplifying
n + -0.2916666667 = 0.817559036

Reorder the terms:
-0.2916666667 + n = 0.817559036

Solving
-0.2916666667 + n = 0.817559036

Solving for variable 'n'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + n = 0.817559036 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + n = 0.817559036 + 0.2916666667
n = 0.817559036 + 0.2916666667

Combine like terms: 0.817559036 + 0.2916666667 = 1.1092257027
n = 1.1092257027

Simplifying
n = 1.1092257027


Subproblem 2
n + -0.2916666667 = -0.817559036

Simplifying
n + -0.2916666667 = -0.817559036

Reorder the terms:
-0.2916666667 + n = -0.817559036

Solving
-0.2916666667 + n = -0.817559036

Solving for variable 'n'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + n = -0.817559036 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + n = -0.817559036 + 0.2916666667
n = -0.817559036 + 0.2916666667

Combine like terms: -0.817559036 + 0.2916666667 = -0.5258923693
n = -0.5258923693

Simplifying
n = -0.5258923693


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.1092257027, -0.5258923693}

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