30x^2-11x-1=0

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Solution for 30x^2-11x-1=0 equation: 


Simplifying
30x2 + -11x + -1 = 0

Reorder the terms:
-1 + -11x + 30x2 = 0

Solving
-1 + -11x + 30x2 = 0

Solving for variable 'x'.

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

Divide each side by '30'.
-0.03333333333 + -0.3666666667x + x2 = 0

Move the constant term to the right:

Add '0.03333333333' to each side of the equation.
-0.03333333333 + -0.3666666667x + 0.03333333333 + x2 = 0 + 0.03333333333

Reorder the terms:
-0.03333333333 + 0.03333333333 + -0.3666666667x + x2 = 0 + 0.03333333333

Combine like terms: -0.03333333333 + 0.03333333333 = 0.00000000000
0.00000000000 + -0.3666666667x + x2 = 0 + 0.03333333333
-0.3666666667x + x2 = 0 + 0.03333333333

Combine like terms: 0 + 0.03333333333 = 0.03333333333
-0.3666666667x + x2 = 0.03333333333

The x term is -0.3666666667x.  Take half its coefficient (-0.1833333334).
Square it (0.03361111114) and add it to both sides.

Add '0.03361111114' to each side of the equation.
-0.3666666667x + 0.03361111114 + x2 = 0.03333333333 + 0.03361111114

Reorder the terms:
0.03361111114 + -0.3666666667x + x2 = 0.03333333333 + 0.03361111114

Combine like terms: 0.03333333333 + 0.03361111114 = 0.06694444447
0.03361111114 + -0.3666666667x + x2 = 0.06694444447

Factor a perfect square on the left side:
(x + -0.1833333334)(x + -0.1833333334) = 0.06694444447

Calculate the square root of the right side: 0.258736245

Break this problem into two subproblems by setting 
(x + -0.1833333334) equal to 0.258736245 and -0.258736245.


Subproblem 1
x + -0.1833333334 = 0.258736245

Simplifying
x + -0.1833333334 = 0.258736245

Reorder the terms:
-0.1833333334 + x = 0.258736245

Solving
-0.1833333334 + x = 0.258736245

Solving for variable 'x'.

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

Add '0.1833333334' to each side of the equation.
-0.1833333334 + 0.1833333334 + x = 0.258736245 + 0.1833333334

Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000
0.0000000000 + x = 0.258736245 + 0.1833333334
x = 0.258736245 + 0.1833333334

Combine like terms: 0.258736245 + 0.1833333334 = 0.4420695784
x = 0.4420695784

Simplifying
x = 0.4420695784


Subproblem 2
x + -0.1833333334 = -0.258736245

Simplifying
x + -0.1833333334 = -0.258736245

Reorder the terms:
-0.1833333334 + x = -0.258736245

Solving
-0.1833333334 + x = -0.258736245

Solving for variable 'x'.

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

Add '0.1833333334' to each side of the equation.
-0.1833333334 + 0.1833333334 + x = -0.258736245 + 0.1833333334

Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000
0.0000000000 + x = -0.258736245 + 0.1833333334
x = -0.258736245 + 0.1833333334

Combine like terms: -0.258736245 + 0.1833333334 = -0.0754029116
x = -0.0754029116

Simplifying
x = -0.0754029116


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4420695784, -0.0754029116}

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