-16x^2+266x-198=0

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Solution for -16x^2+266x-198=0 equation: 


Simplifying
-16x2 + 266x + -198 = 0

Reorder the terms:
-198 + 266x + -16x2 = 0

Solving
-198 + 266x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-99 + 133x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-99 + 133x + -8x2)' equal to zero and attempt to solve:

Simplifying
-99 + 133x + -8x2 = 0

Solving
-99 + 133x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
12.375 + -16.625x + x2 = 0

Move the constant term to the right:

Add '-12.375' to each side of the equation.
12.375 + -16.625x + -12.375 + x2 = 0 + -12.375

Reorder the terms:
12.375 + -12.375 + -16.625x + x2 = 0 + -12.375

Combine like terms: 12.375 + -12.375 = 0.000
0.000 + -16.625x + x2 = 0 + -12.375
-16.625x + x2 = 0 + -12.375

Combine like terms: 0 + -12.375 = -12.375
-16.625x + x2 = -12.375

The x term is -16.625x.  Take half its coefficient (-8.3125).
Square it (69.09765625) and add it to both sides.

Add '69.09765625' to each side of the equation.
-16.625x + 69.09765625 + x2 = -12.375 + 69.09765625

Reorder the terms:
69.09765625 + -16.625x + x2 = -12.375 + 69.09765625

Combine like terms: -12.375 + 69.09765625 = 56.72265625
69.09765625 + -16.625x + x2 = 56.72265625

Factor a perfect square on the left side:
(x + -8.3125)(x + -8.3125) = 56.72265625

Calculate the square root of the right side: 7.5314445

Break this problem into two subproblems by setting 
(x + -8.3125) equal to 7.5314445 and -7.5314445.


Subproblem 1
x + -8.3125 = 7.5314445

Simplifying
x + -8.3125 = 7.5314445

Reorder the terms:
-8.3125 + x = 7.5314445

Solving
-8.3125 + x = 7.5314445

Solving for variable 'x'.

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

Add '8.3125' to each side of the equation.
-8.3125 + 8.3125 + x = 7.5314445 + 8.3125

Combine like terms: -8.3125 + 8.3125 = 0.0000
0.0000 + x = 7.5314445 + 8.3125
x = 7.5314445 + 8.3125

Combine like terms: 7.5314445 + 8.3125 = 15.8439445
x = 15.8439445

Simplifying
x = 15.8439445


Subproblem 2
x + -8.3125 = -7.5314445

Simplifying
x + -8.3125 = -7.5314445

Reorder the terms:
-8.3125 + x = -7.5314445

Solving
-8.3125 + x = -7.5314445

Solving for variable 'x'.

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

Add '8.3125' to each side of the equation.
-8.3125 + 8.3125 + x = -7.5314445 + 8.3125

Combine like terms: -8.3125 + 8.3125 = 0.0000
0.0000 + x = -7.5314445 + 8.3125
x = -7.5314445 + 8.3125

Combine like terms: -7.5314445 + 8.3125 = 0.7810555
x = 0.7810555

Simplifying
x = 0.7810555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.8439445, 0.7810555}
Solution
x = {15.8439445, 0.7810555}

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