-16x^2+212x+22=0

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Solution for -16x^2+212x+22=0 equation: 


Simplifying
-16x2 + 212x + 22 = 0

Reorder the terms:
22 + 212x + -16x2 = 0

Solving
22 + 212x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 106x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + 106x + -8x2)' equal to zero and attempt to solve:

Simplifying
11 + 106x + -8x2 = 0

Solving
11 + 106x + -8x2 = 0

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

Divide each side by '-8'.
-1.375 + -13.25x + x2 = 0

Move the constant term to the right:

Add '1.375' to each side of the equation.
-1.375 + -13.25x + 1.375 + x2 = 0 + 1.375

Reorder the terms:
-1.375 + 1.375 + -13.25x + x2 = 0 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + -13.25x + x2 = 0 + 1.375
-13.25x + x2 = 0 + 1.375

Combine like terms: 0 + 1.375 = 1.375
-13.25x + x2 = 1.375

The x term is -13.25x.  Take half its coefficient (-6.625).
Square it (43.890625) and add it to both sides.

Add '43.890625' to each side of the equation.
-13.25x + 43.890625 + x2 = 1.375 + 43.890625

Reorder the terms:
43.890625 + -13.25x + x2 = 1.375 + 43.890625

Combine like terms: 1.375 + 43.890625 = 45.265625
43.890625 + -13.25x + x2 = 45.265625

Factor a perfect square on the left side:
(x + -6.625)(x + -6.625) = 45.265625

Calculate the square root of the right side: 6.72797332

Break this problem into two subproblems by setting 
(x + -6.625) equal to 6.72797332 and -6.72797332.


Subproblem 1
x + -6.625 = 6.72797332

Simplifying
x + -6.625 = 6.72797332

Reorder the terms:
-6.625 + x = 6.72797332

Solving
-6.625 + x = 6.72797332

Solving for variable 'x'.

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

Add '6.625' to each side of the equation.
-6.625 + 6.625 + x = 6.72797332 + 6.625

Combine like terms: -6.625 + 6.625 = 0.000
0.000 + x = 6.72797332 + 6.625
x = 6.72797332 + 6.625

Combine like terms: 6.72797332 + 6.625 = 13.35297332
x = 13.35297332

Simplifying
x = 13.35297332


Subproblem 2
x + -6.625 = -6.72797332

Simplifying
x + -6.625 = -6.72797332

Reorder the terms:
-6.625 + x = -6.72797332

Solving
-6.625 + x = -6.72797332

Solving for variable 'x'.

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

Add '6.625' to each side of the equation.
-6.625 + 6.625 + x = -6.72797332 + 6.625

Combine like terms: -6.625 + 6.625 = 0.000
0.000 + x = -6.72797332 + 6.625
x = -6.72797332 + 6.625

Combine like terms: -6.72797332 + 6.625 = -0.10297332
x = -0.10297332

Simplifying
x = -0.10297332


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.35297332, -0.10297332}
Solution
x = {13.35297332, -0.10297332}

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