3x^2+69x+180=125

Solution for 3x^2+69x+180=125 equation:

Simplifying
3x2 + 69x + 180 = 125

Reorder the terms:
180 + 69x + 3x2 = 125

Solving
180 + 69x + 3x2 = 125

Solving for variable 'x'.

Reorder the terms:
180 + -125 + 69x + 3x2 = 125 + -125

Combine like terms: 180 + -125 = 55
55 + 69x + 3x2 = 125 + -125

Combine like terms: 125 + -125 = 0
55 + 69x + 3x2 = 0

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

Divide each side by '3'.
18.33333333 + 23x + x2 = 0

Move the constant term to the right:

Add '-18.33333333' to each side of the equation.
18.33333333 + 23x + -18.33333333 + x2 = 0 + -18.33333333

Reorder the terms:
18.33333333 + -18.33333333 + 23x + x2 = 0 + -18.33333333

Combine like terms: 18.33333333 + -18.33333333 = 0.00000000
0.00000000 + 23x + x2 = 0 + -18.33333333
23x + x2 = 0 + -18.33333333

Combine like terms: 0 + -18.33333333 = -18.33333333
23x + x2 = -18.33333333

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = -18.33333333 + 132.25

Reorder the terms:
132.25 + 23x + x2 = -18.33333333 + 132.25

Combine like terms: -18.33333333 + 132.25 = 113.91666667
132.25 + 23x + x2 = 113.91666667

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 113.91666667

Calculate the square root of the right side: 10.673175098

Break this problem into two subproblems by setting 
(x + 11.5) equal to 10.673175098 and -10.673175098.

Subproblem 1
x + 11.5 = 10.673175098

Simplifying
x + 11.5 = 10.673175098

Reorder the terms:
11.5 + x = 10.673175098

Solving
11.5 + x = 10.673175098

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = 10.673175098 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 10.673175098 + -11.5
x = 10.673175098 + -11.5

Combine like terms: 10.673175098 + -11.5 = -0.826824902
x = -0.826824902

Simplifying
x = -0.826824902

Subproblem 2
x + 11.5 = -10.673175098

Simplifying
x + 11.5 = -10.673175098

Reorder the terms:
11.5 + x = -10.673175098

Solving
11.5 + x = -10.673175098

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = -10.673175098 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -10.673175098 + -11.5
x = -10.673175098 + -11.5

Combine like terms: -10.673175098 + -11.5 = -22.173175098
x = -22.173175098

Simplifying
x = -22.173175098

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.826824902, -22.173175098}