16x^2+8x-446=0

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Solution for 16x^2+8x-446=0 equation: 


Simplifying
16x2 + 8x + -446 = 0

Reorder the terms:
-446 + 8x + 16x2 = 0

Solving
-446 + 8x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-223 + 4x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-223 + 4x + 8x2)' equal to zero and attempt to solve:

Simplifying
-223 + 4x + 8x2 = 0

Solving
-223 + 4x + 8x2 = 0

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

Divide each side by '8'.
-27.875 + 0.5x + x2 = 0

Move the constant term to the right:

Add '27.875' to each side of the equation.
-27.875 + 0.5x + 27.875 + x2 = 0 + 27.875

Reorder the terms:
-27.875 + 27.875 + 0.5x + x2 = 0 + 27.875

Combine like terms: -27.875 + 27.875 = 0.000
0.000 + 0.5x + x2 = 0 + 27.875
0.5x + x2 = 0 + 27.875

Combine like terms: 0 + 27.875 = 27.875
0.5x + x2 = 27.875

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 27.875 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 27.875 + 0.0625

Combine like terms: 27.875 + 0.0625 = 27.9375
0.0625 + 0.5x + x2 = 27.9375

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 27.9375

Calculate the square root of the right side: 5.285593628

Break this problem into two subproblems by setting 
(x + 0.25) equal to 5.285593628 and -5.285593628.


Subproblem 1
x + 0.25 = 5.285593628

Simplifying
x + 0.25 = 5.285593628

Reorder the terms:
0.25 + x = 5.285593628

Solving
0.25 + x = 5.285593628

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 5.285593628 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 5.285593628 + -0.25
x = 5.285593628 + -0.25

Combine like terms: 5.285593628 + -0.25 = 5.035593628
x = 5.035593628

Simplifying
x = 5.035593628


Subproblem 2
x + 0.25 = -5.285593628

Simplifying
x + 0.25 = -5.285593628

Reorder the terms:
0.25 + x = -5.285593628

Solving
0.25 + x = -5.285593628

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -5.285593628 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -5.285593628 + -0.25
x = -5.285593628 + -0.25

Combine like terms: -5.285593628 + -0.25 = -5.535593628
x = -5.535593628

Simplifying
x = -5.535593628


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.035593628, -5.535593628}
Solution
x = {5.035593628, -5.535593628}

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