-16X^2+65.5X+5.5=0

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Solution for -16X^2+65.5X+5.5=0 equation: 


Simplifying
-16X2 + 65.5X + 5.5 = 0

Reorder the terms:
5.5 + 65.5X + -16X2 = 0

Solving
5.5 + 65.5X + -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'.
-0.34375 + -4.09375X + X2 = 0

Move the constant term to the right:

Add '0.34375' to each side of the equation.
-0.34375 + -4.09375X + 0.34375 + X2 = 0 + 0.34375

Reorder the terms:
-0.34375 + 0.34375 + -4.09375X + X2 = 0 + 0.34375

Combine like terms: -0.34375 + 0.34375 = 0.00000
0.00000 + -4.09375X + X2 = 0 + 0.34375
-4.09375X + X2 = 0 + 0.34375

Combine like terms: 0 + 0.34375 = 0.34375
-4.09375X + X2 = 0.34375

The X term is -4.09375X.  Take half its coefficient (-2.046875).
Square it (4.189697266) and add it to both sides.

Add '4.189697266' to each side of the equation.
-4.09375X + 4.189697266 + X2 = 0.34375 + 4.189697266

Reorder the terms:
4.189697266 + -4.09375X + X2 = 0.34375 + 4.189697266

Combine like terms: 0.34375 + 4.189697266 = 4.533447266
4.189697266 + -4.09375X + X2 = 4.533447266

Factor a perfect square on the left side:
(X + -2.046875)(X + -2.046875) = 4.533447266

Calculate the square root of the right side: 2.129189345

Break this problem into two subproblems by setting 
(X + -2.046875) equal to 2.129189345 and -2.129189345.


Subproblem 1
X + -2.046875 = 2.129189345

Simplifying
X + -2.046875 = 2.129189345

Reorder the terms:
-2.046875 + X = 2.129189345

Solving
-2.046875 + X = 2.129189345

Solving for variable 'X'.

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

Add '2.046875' to each side of the equation.
-2.046875 + 2.046875 + X = 2.129189345 + 2.046875

Combine like terms: -2.046875 + 2.046875 = 0.000000
0.000000 + X = 2.129189345 + 2.046875
X = 2.129189345 + 2.046875

Combine like terms: 2.129189345 + 2.046875 = 4.176064345
X = 4.176064345

Simplifying
X = 4.176064345


Subproblem 2
X + -2.046875 = -2.129189345

Simplifying
X + -2.046875 = -2.129189345

Reorder the terms:
-2.046875 + X = -2.129189345

Solving
-2.046875 + X = -2.129189345

Solving for variable 'X'.

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

Add '2.046875' to each side of the equation.
-2.046875 + 2.046875 + X = -2.129189345 + 2.046875

Combine like terms: -2.046875 + 2.046875 = 0.000000
0.000000 + X = -2.129189345 + 2.046875
X = -2.129189345 + 2.046875

Combine like terms: -2.129189345 + 2.046875 = -0.082314345
X = -0.082314345

Simplifying
X = -0.082314345


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {4.176064345, -0.082314345}

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