x^2+35x+60=0

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Solution for x^2+35x+60=0 equation: 


Simplifying
x2 + 35x + 60 = 0

Reorder the terms:
60 + 35x + x2 = 0

Solving
60 + 35x + x2 = 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 + 35x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 35x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 35x + x2 = 0 + -60
35x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
35x + x2 = -60

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = -60 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -60 + 306.25

Combine like terms: -60 + 306.25 = 246.25
306.25 + 35x + x2 = 246.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 246.25

Calculate the square root of the right side: 15.692354826

Break this problem into two subproblems by setting 
(x + 17.5) equal to 15.692354826 and -15.692354826.


Subproblem 1
x + 17.5 = 15.692354826

Simplifying
x + 17.5 = 15.692354826

Reorder the terms:
17.5 + x = 15.692354826

Solving
17.5 + x = 15.692354826

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 15.692354826 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 15.692354826 + -17.5
x = 15.692354826 + -17.5

Combine like terms: 15.692354826 + -17.5 = -1.807645174
x = -1.807645174

Simplifying
x = -1.807645174


Subproblem 2
x + 17.5 = -15.692354826

Simplifying
x + 17.5 = -15.692354826

Reorder the terms:
17.5 + x = -15.692354826

Solving
17.5 + x = -15.692354826

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -15.692354826 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -15.692354826 + -17.5
x = -15.692354826 + -17.5

Combine like terms: -15.692354826 + -17.5 = -33.192354826
x = -33.192354826

Simplifying
x = -33.192354826


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.807645174, -33.192354826}

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