1x^2+36x+60=0

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Solution for 1x^2+36x+60=0 equation: 


Simplifying
1x2 + 36x + 60 = 0

Reorder the terms:
60 + 36x + 1x2 = 0

Solving
60 + 36x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + 36x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 36x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 36x + x2 = 0 + -60
36x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
36x + x2 = -60

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = -60 + 324

Reorder the terms:
324 + 36x + x2 = -60 + 324

Combine like terms: -60 + 324 = 264
324 + 36x + x2 = 264

Factor a perfect square on the left side:
(x + 18)(x + 18) = 264

Calculate the square root of the right side: 16.248076809

Break this problem into two subproblems by setting 
(x + 18) equal to 16.248076809 and -16.248076809.


Subproblem 1
x + 18 = 16.248076809

Simplifying
x + 18 = 16.248076809

Reorder the terms:
18 + x = 16.248076809

Solving
18 + x = 16.248076809

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = 16.248076809 + -18

Combine like terms: 18 + -18 = 0
0 + x = 16.248076809 + -18
x = 16.248076809 + -18

Combine like terms: 16.248076809 + -18 = -1.751923191
x = -1.751923191

Simplifying
x = -1.751923191


Subproblem 2
x + 18 = -16.248076809

Simplifying
x + 18 = -16.248076809

Reorder the terms:
18 + x = -16.248076809

Solving
18 + x = -16.248076809

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = -16.248076809 + -18

Combine like terms: 18 + -18 = 0
0 + x = -16.248076809 + -18
x = -16.248076809 + -18

Combine like terms: -16.248076809 + -18 = -34.248076809
x = -34.248076809

Simplifying
x = -34.248076809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.751923191, -34.248076809}

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