16x^2+14x+2=0

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Solution for 16x^2+14x+2=0 equation: 


Simplifying
16x2 + 14x + 2 = 0

Reorder the terms:
2 + 14x + 16x2 = 0

Solving
2 + 14x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 7x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 7x + 8x2)' equal to zero and attempt to solve:

Simplifying
1 + 7x + 8x2 = 0

Solving
1 + 7x + 8x2 = 0

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

Divide each side by '8'.
0.125 + 0.875x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 0.875x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 0.875x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 0.875x + x2 = 0 + -0.125
0.875x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
0.875x + x2 = -0.125

The x term is 0.875x.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875x + 0.19140625 + x2 = -0.125 + 0.19140625

Reorder the terms:
0.19140625 + 0.875x + x2 = -0.125 + 0.19140625

Combine like terms: -0.125 + 0.19140625 = 0.06640625
0.19140625 + 0.875x + x2 = 0.06640625

Factor a perfect square on the left side:
(x + 0.4375)(x + 0.4375) = 0.06640625

Calculate the square root of the right side: 0.257694102

Break this problem into two subproblems by setting 
(x + 0.4375) equal to 0.257694102 and -0.257694102.


Subproblem 1
x + 0.4375 = 0.257694102

Simplifying
x + 0.4375 = 0.257694102

Reorder the terms:
0.4375 + x = 0.257694102

Solving
0.4375 + x = 0.257694102

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = 0.257694102 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = 0.257694102 + -0.4375
x = 0.257694102 + -0.4375

Combine like terms: 0.257694102 + -0.4375 = -0.179805898
x = -0.179805898

Simplifying
x = -0.179805898


Subproblem 2
x + 0.4375 = -0.257694102

Simplifying
x + 0.4375 = -0.257694102

Reorder the terms:
0.4375 + x = -0.257694102

Solving
0.4375 + x = -0.257694102

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = -0.257694102 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = -0.257694102 + -0.4375
x = -0.257694102 + -0.4375

Combine like terms: -0.257694102 + -0.4375 = -0.695194102
x = -0.695194102

Simplifying
x = -0.695194102


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.179805898, -0.695194102}
Solution
x = {-0.179805898, -0.695194102}

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