16x^2+180x+14=0

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Solution for 16x^2+180x+14=0 equation: 


Simplifying
16x2 + 180x + 14 = 0

Reorder the terms:
14 + 180x + 16x2 = 0

Solving
14 + 180x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 90x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 90x + 8x2)' equal to zero and attempt to solve:

Simplifying
7 + 90x + 8x2 = 0

Solving
7 + 90x + 8x2 = 0

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

Divide each side by '8'.
0.875 + 11.25x + x2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + 11.25x + -0.875 + x2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + 11.25x + x2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + 11.25x + x2 = 0 + -0.875
11.25x + x2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
11.25x + x2 = -0.875

The x term is 11.25x.  Take half its coefficient (5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
11.25x + 31.640625 + x2 = -0.875 + 31.640625

Reorder the terms:
31.640625 + 11.25x + x2 = -0.875 + 31.640625

Combine like terms: -0.875 + 31.640625 = 30.765625
31.640625 + 11.25x + x2 = 30.765625

Factor a perfect square on the left side:
(x + 5.625)(x + 5.625) = 30.765625

Calculate the square root of the right side: 5.546676933

Break this problem into two subproblems by setting 
(x + 5.625) equal to 5.546676933 and -5.546676933.


Subproblem 1
x + 5.625 = 5.546676933

Simplifying
x + 5.625 = 5.546676933

Reorder the terms:
5.625 + x = 5.546676933

Solving
5.625 + x = 5.546676933

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = 5.546676933 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = 5.546676933 + -5.625
x = 5.546676933 + -5.625

Combine like terms: 5.546676933 + -5.625 = -0.078323067
x = -0.078323067

Simplifying
x = -0.078323067


Subproblem 2
x + 5.625 = -5.546676933

Simplifying
x + 5.625 = -5.546676933

Reorder the terms:
5.625 + x = -5.546676933

Solving
5.625 + x = -5.546676933

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = -5.546676933 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = -5.546676933 + -5.625
x = -5.546676933 + -5.625

Combine like terms: -5.546676933 + -5.625 = -11.171676933
x = -11.171676933

Simplifying
x = -11.171676933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.078323067, -11.171676933}
Solution
x = {-0.078323067, -11.171676933}

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