16x^2+120x+4=6

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Solution for 16x^2+120x+4=6 equation: 


Simplifying
16x2 + 120x + 4 = 6

Reorder the terms:
4 + 120x + 16x2 = 6

Solving
4 + 120x + 16x2 = 6

Solving for variable 'x'.

Reorder the terms:
4 + -6 + 120x + 16x2 = 6 + -6

Combine like terms: 4 + -6 = -2
-2 + 120x + 16x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-2 + 120x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 60x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 60x + 8x2)' equal to zero and attempt to solve:

Simplifying
-1 + 60x + 8x2 = 0

Solving
-1 + 60x + 8x2 = 0

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

Divide each side by '8'.
-0.125 + 7.5x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 7.5x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 7.5x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 7.5x + x2 = 0 + 0.125
7.5x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
7.5x + x2 = 0.125

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 0.125 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 0.125 + 14.0625

Combine like terms: 0.125 + 14.0625 = 14.1875
14.0625 + 7.5x + x2 = 14.1875

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 14.1875

Calculate the square root of the right side: 3.766629793

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.766629793 and -3.766629793.


Subproblem 1
x + 3.75 = 3.766629793

Simplifying
x + 3.75 = 3.766629793

Reorder the terms:
3.75 + x = 3.766629793

Solving
3.75 + x = 3.766629793

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.766629793 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.766629793 + -3.75
x = 3.766629793 + -3.75

Combine like terms: 3.766629793 + -3.75 = 0.016629793
x = 0.016629793

Simplifying
x = 0.016629793


Subproblem 2
x + 3.75 = -3.766629793

Simplifying
x + 3.75 = -3.766629793

Reorder the terms:
3.75 + x = -3.766629793

Solving
3.75 + x = -3.766629793

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.766629793 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.766629793 + -3.75
x = -3.766629793 + -3.75

Combine like terms: -3.766629793 + -3.75 = -7.516629793
x = -7.516629793

Simplifying
x = -7.516629793


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.016629793, -7.516629793}
Solution
x = {0.016629793, -7.516629793}

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