300x^2-120x-8=0

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Solution for 300x^2-120x-8=0 equation: 


Simplifying
300x2 + -120x + -8 = 0

Reorder the terms:
-8 + -120x + 300x2 = 0

Solving
-8 + -120x + 300x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -30x + 75x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -30x + 75x2)' equal to zero and attempt to solve:

Simplifying
-2 + -30x + 75x2 = 0

Solving
-2 + -30x + 75x2 = 0

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

Divide each side by '75'.
-0.02666666667 + -0.4x + x2 = 0

Move the constant term to the right:

Add '0.02666666667' to each side of the equation.
-0.02666666667 + -0.4x + 0.02666666667 + x2 = 0 + 0.02666666667

Reorder the terms:
-0.02666666667 + 0.02666666667 + -0.4x + x2 = 0 + 0.02666666667

Combine like terms: -0.02666666667 + 0.02666666667 = 0.00000000000
0.00000000000 + -0.4x + x2 = 0 + 0.02666666667
-0.4x + x2 = 0 + 0.02666666667

Combine like terms: 0 + 0.02666666667 = 0.02666666667
-0.4x + x2 = 0.02666666667

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 0.02666666667 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 0.02666666667 + 0.04

Combine like terms: 0.02666666667 + 0.04 = 0.06666666667
0.04 + -0.4x + x2 = 0.06666666667

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 0.06666666667

Calculate the square root of the right side: 0.25819889

Break this problem into two subproblems by setting 
(x + -0.2) equal to 0.25819889 and -0.25819889.


Subproblem 1
x + -0.2 = 0.25819889

Simplifying
x + -0.2 = 0.25819889

Reorder the terms:
-0.2 + x = 0.25819889

Solving
-0.2 + x = 0.25819889

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = 0.25819889 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = 0.25819889 + 0.2
x = 0.25819889 + 0.2

Combine like terms: 0.25819889 + 0.2 = 0.45819889
x = 0.45819889

Simplifying
x = 0.45819889


Subproblem 2
x + -0.2 = -0.25819889

Simplifying
x + -0.2 = -0.25819889

Reorder the terms:
-0.2 + x = -0.25819889

Solving
-0.2 + x = -0.25819889

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = -0.25819889 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = -0.25819889 + 0.2
x = -0.25819889 + 0.2

Combine like terms: -0.25819889 + 0.2 = -0.05819889
x = -0.05819889

Simplifying
x = -0.05819889


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.45819889, -0.05819889}
Solution
x = {0.45819889, -0.05819889}

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