-16x^2+201x-93=0

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Solution for -16x^2+201x-93=0 equation: 


Simplifying
-16x2 + 201x + -93 = 0

Reorder the terms:
-93 + 201x + -16x2 = 0

Solving
-93 + 201x + -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'.
5.8125 + -12.5625x + x2 = 0

Move the constant term to the right:

Add '-5.8125' to each side of the equation.
5.8125 + -12.5625x + -5.8125 + x2 = 0 + -5.8125

Reorder the terms:
5.8125 + -5.8125 + -12.5625x + x2 = 0 + -5.8125

Combine like terms: 5.8125 + -5.8125 = 0.0000
0.0000 + -12.5625x + x2 = 0 + -5.8125
-12.5625x + x2 = 0 + -5.8125

Combine like terms: 0 + -5.8125 = -5.8125
-12.5625x + x2 = -5.8125

The x term is -12.5625x.  Take half its coefficient (-6.28125).
Square it (39.45410156) and add it to both sides.

Add '39.45410156' to each side of the equation.
-12.5625x + 39.45410156 + x2 = -5.8125 + 39.45410156

Reorder the terms:
39.45410156 + -12.5625x + x2 = -5.8125 + 39.45410156

Combine like terms: -5.8125 + 39.45410156 = 33.64160156
39.45410156 + -12.5625x + x2 = 33.64160156

Factor a perfect square on the left side:
(x + -6.28125)(x + -6.28125) = 33.64160156

Calculate the square root of the right side: 5.800138064

Break this problem into two subproblems by setting 
(x + -6.28125) equal to 5.800138064 and -5.800138064.


Subproblem 1
x + -6.28125 = 5.800138064

Simplifying
x + -6.28125 = 5.800138064

Reorder the terms:
-6.28125 + x = 5.800138064

Solving
-6.28125 + x = 5.800138064

Solving for variable 'x'.

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

Add '6.28125' to each side of the equation.
-6.28125 + 6.28125 + x = 5.800138064 + 6.28125

Combine like terms: -6.28125 + 6.28125 = 0.00000
0.00000 + x = 5.800138064 + 6.28125
x = 5.800138064 + 6.28125

Combine like terms: 5.800138064 + 6.28125 = 12.081388064
x = 12.081388064

Simplifying
x = 12.081388064


Subproblem 2
x + -6.28125 = -5.800138064

Simplifying
x + -6.28125 = -5.800138064

Reorder the terms:
-6.28125 + x = -5.800138064

Solving
-6.28125 + x = -5.800138064

Solving for variable 'x'.

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

Add '6.28125' to each side of the equation.
-6.28125 + 6.28125 + x = -5.800138064 + 6.28125

Combine like terms: -6.28125 + 6.28125 = 0.00000
0.00000 + x = -5.800138064 + 6.28125
x = -5.800138064 + 6.28125

Combine like terms: -5.800138064 + 6.28125 = 0.481111936
x = 0.481111936

Simplifying
x = 0.481111936


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.081388064, 0.481111936}

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