18x^2+134x-115=0

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Solution for 18x^2+134x-115=0 equation: 


Simplifying
18x2 + 134x + -115 = 0

Reorder the terms:
-115 + 134x + 18x2 = 0

Solving
-115 + 134x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
-6.388888889 + 7.444444444x + x2 = 0

Move the constant term to the right:

Add '6.388888889' to each side of the equation.
-6.388888889 + 7.444444444x + 6.388888889 + x2 = 0 + 6.388888889

Reorder the terms:
-6.388888889 + 6.388888889 + 7.444444444x + x2 = 0 + 6.388888889

Combine like terms: -6.388888889 + 6.388888889 = 0.000000000
0.000000000 + 7.444444444x + x2 = 0 + 6.388888889
7.444444444x + x2 = 0 + 6.388888889

Combine like terms: 0 + 6.388888889 = 6.388888889
7.444444444x + x2 = 6.388888889

The x term is 7.444444444x.  Take half its coefficient (3.722222222).
Square it (13.85493827) and add it to both sides.

Add '13.85493827' to each side of the equation.
7.444444444x + 13.85493827 + x2 = 6.388888889 + 13.85493827

Reorder the terms:
13.85493827 + 7.444444444x + x2 = 6.388888889 + 13.85493827

Combine like terms: 6.388888889 + 13.85493827 = 20.243827159
13.85493827 + 7.444444444x + x2 = 20.243827159

Factor a perfect square on the left side:
(x + 3.722222222)(x + 3.722222222) = 20.243827159

Calculate the square root of the right side: 4.499314077

Break this problem into two subproblems by setting 
(x + 3.722222222) equal to 4.499314077 and -4.499314077.


Subproblem 1
x + 3.722222222 = 4.499314077

Simplifying
x + 3.722222222 = 4.499314077

Reorder the terms:
3.722222222 + x = 4.499314077

Solving
3.722222222 + x = 4.499314077

Solving for variable 'x'.

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

Add '-3.722222222' to each side of the equation.
3.722222222 + -3.722222222 + x = 4.499314077 + -3.722222222

Combine like terms: 3.722222222 + -3.722222222 = 0.000000000
0.000000000 + x = 4.499314077 + -3.722222222
x = 4.499314077 + -3.722222222

Combine like terms: 4.499314077 + -3.722222222 = 0.777091855
x = 0.777091855

Simplifying
x = 0.777091855


Subproblem 2
x + 3.722222222 = -4.499314077

Simplifying
x + 3.722222222 = -4.499314077

Reorder the terms:
3.722222222 + x = -4.499314077

Solving
3.722222222 + x = -4.499314077

Solving for variable 'x'.

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

Add '-3.722222222' to each side of the equation.
3.722222222 + -3.722222222 + x = -4.499314077 + -3.722222222

Combine like terms: 3.722222222 + -3.722222222 = 0.000000000
0.000000000 + x = -4.499314077 + -3.722222222
x = -4.499314077 + -3.722222222

Combine like terms: -4.499314077 + -3.722222222 = -8.221536299
x = -8.221536299

Simplifying
x = -8.221536299


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.777091855, -8.221536299}

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