-30x^2+192x-9=0

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Solution for -30x^2+192x-9=0 equation: 


Simplifying
-30x2 + 192x + -9 = 0

Reorder the terms:
-9 + 192x + -30x2 = 0

Solving
-9 + 192x + -30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 64x + -10x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + 64x + -10x2)' equal to zero and attempt to solve:

Simplifying
-3 + 64x + -10x2 = 0

Solving
-3 + 64x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
0.3 + -6.4x + x2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + -6.4x + -0.3 + x2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + -6.4x + x2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -6.4x + x2 = 0.0 + -0.3
-6.4x + x2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
-6.4x + x2 = -0.3

The x term is -6.4x.  Take half its coefficient (-3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
-6.4x + 10.24 + x2 = -0.3 + 10.24

Reorder the terms:
10.24 + -6.4x + x2 = -0.3 + 10.24

Combine like terms: -0.3 + 10.24 = 9.94
10.24 + -6.4x + x2 = 9.94

Factor a perfect square on the left side:
(x + -3.2)(x + -3.2) = 9.94

Calculate the square root of the right side: 3.152776554

Break this problem into two subproblems by setting 
(x + -3.2) equal to 3.152776554 and -3.152776554.


Subproblem 1
x + -3.2 = 3.152776554

Simplifying
x + -3.2 = 3.152776554

Reorder the terms:
-3.2 + x = 3.152776554

Solving
-3.2 + x = 3.152776554

Solving for variable 'x'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + x = 3.152776554 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + x = 3.152776554 + 3.2
x = 3.152776554 + 3.2

Combine like terms: 3.152776554 + 3.2 = 6.352776554
x = 6.352776554

Simplifying
x = 6.352776554


Subproblem 2
x + -3.2 = -3.152776554

Simplifying
x + -3.2 = -3.152776554

Reorder the terms:
-3.2 + x = -3.152776554

Solving
-3.2 + x = -3.152776554

Solving for variable 'x'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + x = -3.152776554 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + x = -3.152776554 + 3.2
x = -3.152776554 + 3.2

Combine like terms: -3.152776554 + 3.2 = 0.047223446
x = 0.047223446

Simplifying
x = 0.047223446


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.352776554, 0.047223446}
Solution
x = {6.352776554, 0.047223446}

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