x^2+24x+60=0

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Solution for x^2+24x+60=0 equation: 


Simplifying
x2 + 24x + 60 = 0

Reorder the terms:
60 + 24x + x2 = 0

Solving
60 + 24x + 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 + 24x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 24x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 24x + x2 = 0 + -60
24x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
24x + x2 = -60

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = -60 + 144

Reorder the terms:
144 + 24x + x2 = -60 + 144

Combine like terms: -60 + 144 = 84
144 + 24x + x2 = 84

Factor a perfect square on the left side:
(x + 12)(x + 12) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + 12) equal to 9.16515139 and -9.16515139.


Subproblem 1
x + 12 = 9.16515139

Simplifying
x + 12 = 9.16515139

Reorder the terms:
12 + x = 9.16515139

Solving
12 + x = 9.16515139

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 9.16515139 + -12

Combine like terms: 12 + -12 = 0
0 + x = 9.16515139 + -12
x = 9.16515139 + -12

Combine like terms: 9.16515139 + -12 = -2.83484861
x = -2.83484861

Simplifying
x = -2.83484861


Subproblem 2
x + 12 = -9.16515139

Simplifying
x + 12 = -9.16515139

Reorder the terms:
12 + x = -9.16515139

Solving
12 + x = -9.16515139

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -9.16515139 + -12

Combine like terms: 12 + -12 = 0
0 + x = -9.16515139 + -12
x = -9.16515139 + -12

Combine like terms: -9.16515139 + -12 = -21.16515139
x = -21.16515139

Simplifying
x = -21.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.83484861, -21.16515139}

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