180x^2-60x-119=0

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Solution for 180x^2-60x-119=0 equation: 


Simplifying
180x2 + -60x + -119 = 0

Reorder the terms:
-119 + -60x + 180x2 = 0

Solving
-119 + -60x + 180x2 = 0

Solving for variable 'x'.

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

Divide each side by '180'.
-0.6611111111 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.6611111111' to each side of the equation.
-0.6611111111 + -0.3333333333x + 0.6611111111 + x2 = 0 + 0.6611111111

Reorder the terms:
-0.6611111111 + 0.6611111111 + -0.3333333333x + x2 = 0 + 0.6611111111

Combine like terms: -0.6611111111 + 0.6611111111 = 0.0000000000
0.0000000000 + -0.3333333333x + x2 = 0 + 0.6611111111
-0.3333333333x + x2 = 0 + 0.6611111111

Combine like terms: 0 + 0.6611111111 = 0.6611111111
-0.3333333333x + x2 = 0.6611111111

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 0.6611111111 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 0.6611111111 + 0.02777777779

Combine like terms: 0.6611111111 + 0.02777777779 = 0.68888888889
0.02777777779 + -0.3333333333x + x2 = 0.68888888889

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 0.68888888889

Calculate the square root of the right side: 0.829993307

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 0.829993307 and -0.829993307.


Subproblem 1
x + -0.1666666667 = 0.829993307

Simplifying
x + -0.1666666667 = 0.829993307

Reorder the terms:
-0.1666666667 + x = 0.829993307

Solving
-0.1666666667 + x = 0.829993307

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 0.829993307 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 0.829993307 + 0.1666666667
x = 0.829993307 + 0.1666666667

Combine like terms: 0.829993307 + 0.1666666667 = 0.9966599737
x = 0.9966599737

Simplifying
x = 0.9966599737


Subproblem 2
x + -0.1666666667 = -0.829993307

Simplifying
x + -0.1666666667 = -0.829993307

Reorder the terms:
-0.1666666667 + x = -0.829993307

Solving
-0.1666666667 + x = -0.829993307

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -0.829993307 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -0.829993307 + 0.1666666667
x = -0.829993307 + 0.1666666667

Combine like terms: -0.829993307 + 0.1666666667 = -0.6633266403
x = -0.6633266403

Simplifying
x = -0.6633266403


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9966599737, -0.6633266403}

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