36x^2+24x-1=0

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Solution for 36x^2+24x-1=0 equation: 


Simplifying
36x2 + 24x + -1 = 0

Reorder the terms:
-1 + 24x + 36x2 = 0

Solving
-1 + 24x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
-0.02777777778 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.02777777778' to each side of the equation.
-0.02777777778 + 0.6666666667x + 0.02777777778 + x2 = 0 + 0.02777777778

Reorder the terms:
-0.02777777778 + 0.02777777778 + 0.6666666667x + x2 = 0 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + 0.6666666667x + x2 = 0 + 0.02777777778
0.6666666667x + x2 = 0 + 0.02777777778

Combine like terms: 0 + 0.02777777778 = 0.02777777778
0.6666666667x + x2 = 0.02777777778

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.02777777778 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.02777777778 + 0.1111111112

Combine like terms: 0.02777777778 + 0.1111111112 = 0.13888888898
0.1111111112 + 0.6666666667x + x2 = 0.13888888898

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.13888888898

Calculate the square root of the right side: 0.372677996

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.372677996 and -0.372677996.


Subproblem 1
x + 0.3333333334 = 0.372677996

Simplifying
x + 0.3333333334 = 0.372677996

Reorder the terms:
0.3333333334 + x = 0.372677996

Solving
0.3333333334 + x = 0.372677996

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.372677996 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.372677996 + -0.3333333334
x = 0.372677996 + -0.3333333334

Combine like terms: 0.372677996 + -0.3333333334 = 0.0393446626
x = 0.0393446626

Simplifying
x = 0.0393446626


Subproblem 2
x + 0.3333333334 = -0.372677996

Simplifying
x + 0.3333333334 = -0.372677996

Reorder the terms:
0.3333333334 + x = -0.372677996

Solving
0.3333333334 + x = -0.372677996

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.372677996 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.372677996 + -0.3333333334
x = -0.372677996 + -0.3333333334

Combine like terms: -0.372677996 + -0.3333333334 = -0.7060113294
x = -0.7060113294

Simplifying
x = -0.7060113294


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0393446626, -0.7060113294}

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