120x-16x^2-190=0

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Solution for 120x-16x^2-190=0 equation: 


Simplifying
120x + -16x2 + -190 = 0

Reorder the terms:
-190 + 120x + -16x2 = 0

Solving
-190 + 120x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-95 + 60x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-95 + 60x + -8x2)' equal to zero and attempt to solve:

Simplifying
-95 + 60x + -8x2 = 0

Solving
-95 + 60x + -8x2 = 0

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

Divide each side by '-8'.
11.875 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-11.875' to each side of the equation.
11.875 + -7.5x + -11.875 + x2 = 0 + -11.875

Reorder the terms:
11.875 + -11.875 + -7.5x + x2 = 0 + -11.875

Combine like terms: 11.875 + -11.875 = 0.000
0.000 + -7.5x + x2 = 0 + -11.875
-7.5x + x2 = 0 + -11.875

Combine like terms: 0 + -11.875 = -11.875
-7.5x + x2 = -11.875

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 = -11.875 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -11.875 + 14.0625

Combine like terms: -11.875 + 14.0625 = 2.1875
14.0625 + -7.5x + x2 = 2.1875

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 2.1875

Calculate the square root of the right side: 1.479019946

Break this problem into two subproblems by setting 
(x + -3.75) equal to 1.479019946 and -1.479019946.


Subproblem 1
x + -3.75 = 1.479019946

Simplifying
x + -3.75 = 1.479019946

Reorder the terms:
-3.75 + x = 1.479019946

Solving
-3.75 + x = 1.479019946

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 = 1.479019946 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 1.479019946 + 3.75
x = 1.479019946 + 3.75

Combine like terms: 1.479019946 + 3.75 = 5.229019946
x = 5.229019946

Simplifying
x = 5.229019946


Subproblem 2
x + -3.75 = -1.479019946

Simplifying
x + -3.75 = -1.479019946

Reorder the terms:
-3.75 + x = -1.479019946

Solving
-3.75 + x = -1.479019946

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 = -1.479019946 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -1.479019946 + 3.75
x = -1.479019946 + 3.75

Combine like terms: -1.479019946 + 3.75 = 2.270980054
x = 2.270980054

Simplifying
x = 2.270980054


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.229019946, 2.270980054}
Solution
x = {5.229019946, 2.270980054}

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