12z^2-1z-158=0

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Solution for 12z^2-1z-158=0 equation: 


Simplifying
12z2 + -1z + -158 = 0

Reorder the terms:
-158 + -1z + 12z2 = 0

Solving
-158 + -1z + 12z2 = 0

Solving for variable 'z'.

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

Divide each side by '12'.
-13.16666667 + -0.08333333333z + z2 = 0

Move the constant term to the right:

Add '13.16666667' to each side of the equation.
-13.16666667 + -0.08333333333z + 13.16666667 + z2 = 0 + 13.16666667

Reorder the terms:
-13.16666667 + 13.16666667 + -0.08333333333z + z2 = 0 + 13.16666667

Combine like terms: -13.16666667 + 13.16666667 = 0.00000000
0.00000000 + -0.08333333333z + z2 = 0 + 13.16666667
-0.08333333333z + z2 = 0 + 13.16666667

Combine like terms: 0 + 13.16666667 = 13.16666667
-0.08333333333z + z2 = 13.16666667

The z term is -0.08333333333z.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333z + 0.001736111111 + z2 = 13.16666667 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333z + z2 = 13.16666667 + 0.001736111111

Combine like terms: 13.16666667 + 0.001736111111 = 13.168402781111
0.001736111111 + -0.08333333333z + z2 = 13.168402781111

Factor a perfect square on the left side:
(z + -0.04166666667)(z + -0.04166666667) = 13.168402781111

Calculate the square root of the right side: 3.628829395

Break this problem into two subproblems by setting 
(z + -0.04166666667) equal to 3.628829395 and -3.628829395.


Subproblem 1
z + -0.04166666667 = 3.628829395

Simplifying
z + -0.04166666667 = 3.628829395

Reorder the terms:
-0.04166666667 + z = 3.628829395

Solving
-0.04166666667 + z = 3.628829395

Solving for variable 'z'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + z = 3.628829395 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + z = 3.628829395 + 0.04166666667
z = 3.628829395 + 0.04166666667

Combine like terms: 3.628829395 + 0.04166666667 = 3.67049606167
z = 3.67049606167

Simplifying
z = 3.67049606167


Subproblem 2
z + -0.04166666667 = -3.628829395

Simplifying
z + -0.04166666667 = -3.628829395

Reorder the terms:
-0.04166666667 + z = -3.628829395

Solving
-0.04166666667 + z = -3.628829395

Solving for variable 'z'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + z = -3.628829395 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + z = -3.628829395 + 0.04166666667
z = -3.628829395 + 0.04166666667

Combine like terms: -3.628829395 + 0.04166666667 = -3.58716272833
z = -3.58716272833

Simplifying
z = -3.58716272833


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {3.67049606167, -3.58716272833}

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