-16x^2+204x-111=0

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Solution for -16x^2+204x-111=0 equation: 


Simplifying
-16x2 + 204x + -111 = 0

Reorder the terms:
-111 + 204x + -16x2 = 0

Solving
-111 + 204x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
6.9375 + -12.75x + x2 = 0

Move the constant term to the right:

Add '-6.9375' to each side of the equation.
6.9375 + -12.75x + -6.9375 + x2 = 0 + -6.9375

Reorder the terms:
6.9375 + -6.9375 + -12.75x + x2 = 0 + -6.9375

Combine like terms: 6.9375 + -6.9375 = 0.0000
0.0000 + -12.75x + x2 = 0 + -6.9375
-12.75x + x2 = 0 + -6.9375

Combine like terms: 0 + -6.9375 = -6.9375
-12.75x + x2 = -6.9375

The x term is -12.75x.  Take half its coefficient (-6.375).
Square it (40.640625) and add it to both sides.

Add '40.640625' to each side of the equation.
-12.75x + 40.640625 + x2 = -6.9375 + 40.640625

Reorder the terms:
40.640625 + -12.75x + x2 = -6.9375 + 40.640625

Combine like terms: -6.9375 + 40.640625 = 33.703125
40.640625 + -12.75x + x2 = 33.703125

Factor a perfect square on the left side:
(x + -6.375)(x + -6.375) = 33.703125

Calculate the square root of the right side: 5.80543926

Break this problem into two subproblems by setting 
(x + -6.375) equal to 5.80543926 and -5.80543926.


Subproblem 1
x + -6.375 = 5.80543926

Simplifying
x + -6.375 = 5.80543926

Reorder the terms:
-6.375 + x = 5.80543926

Solving
-6.375 + x = 5.80543926

Solving for variable 'x'.

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

Add '6.375' to each side of the equation.
-6.375 + 6.375 + x = 5.80543926 + 6.375

Combine like terms: -6.375 + 6.375 = 0.000
0.000 + x = 5.80543926 + 6.375
x = 5.80543926 + 6.375

Combine like terms: 5.80543926 + 6.375 = 12.18043926
x = 12.18043926

Simplifying
x = 12.18043926


Subproblem 2
x + -6.375 = -5.80543926

Simplifying
x + -6.375 = -5.80543926

Reorder the terms:
-6.375 + x = -5.80543926

Solving
-6.375 + x = -5.80543926

Solving for variable 'x'.

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

Add '6.375' to each side of the equation.
-6.375 + 6.375 + x = -5.80543926 + 6.375

Combine like terms: -6.375 + 6.375 = 0.000
0.000 + x = -5.80543926 + 6.375
x = -5.80543926 + 6.375

Combine like terms: -5.80543926 + 6.375 = 0.56956074
x = 0.56956074

Simplifying
x = 0.56956074


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.18043926, 0.56956074}

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