36x^2+12x+-17=0

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Solution for 36x^2+12x+-17=0 equation: 


Simplifying
36x2 + 12x + -17 = 0

Reorder the terms:
-17 + 12x + 36x2 = 0

Solving
-17 + 12x + 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'.
-0.4722222222 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.4722222222' to each side of the equation.
-0.4722222222 + 0.3333333333x + 0.4722222222 + x2 = 0 + 0.4722222222

Reorder the terms:
-0.4722222222 + 0.4722222222 + 0.3333333333x + x2 = 0 + 0.4722222222

Combine like terms: -0.4722222222 + 0.4722222222 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + 0.4722222222
0.3333333333x + x2 = 0 + 0.4722222222

Combine like terms: 0 + 0.4722222222 = 0.4722222222
0.3333333333x + x2 = 0.4722222222

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.4722222222 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.4722222222 + 0.02777777779

Combine like terms: 0.4722222222 + 0.02777777779 = 0.49999999999
0.02777777779 + 0.3333333333x + x2 = 0.49999999999

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.49999999999

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.707106781 and -0.707106781.


Subproblem 1
x + 0.1666666667 = 0.707106781

Simplifying
x + 0.1666666667 = 0.707106781

Reorder the terms:
0.1666666667 + x = 0.707106781

Solving
0.1666666667 + x = 0.707106781

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.707106781 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.707106781 + -0.1666666667
x = 0.707106781 + -0.1666666667

Combine like terms: 0.707106781 + -0.1666666667 = 0.5404401143
x = 0.5404401143

Simplifying
x = 0.5404401143


Subproblem 2
x + 0.1666666667 = -0.707106781

Simplifying
x + 0.1666666667 = -0.707106781

Reorder the terms:
0.1666666667 + x = -0.707106781

Solving
0.1666666667 + x = -0.707106781

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.707106781 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.707106781 + -0.1666666667
x = -0.707106781 + -0.1666666667

Combine like terms: -0.707106781 + -0.1666666667 = -0.8737734477
x = -0.8737734477

Simplifying
x = -0.8737734477


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5404401143, -0.8737734477}

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