x^2+48x+60=0

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Solution for x^2+48x+60=0 equation: 


Simplifying
x2 + 48x + 60 = 0

Reorder the terms:
60 + 48x + x2 = 0

Solving
60 + 48x + 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 + 48x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 48x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 48x + x2 = 0 + -60
48x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
48x + x2 = -60

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = -60 + 576

Reorder the terms:
576 + 48x + x2 = -60 + 576

Combine like terms: -60 + 576 = 516
576 + 48x + x2 = 516

Factor a perfect square on the left side:
(x + 24)(x + 24) = 516

Calculate the square root of the right side: 22.715633383

Break this problem into two subproblems by setting 
(x + 24) equal to 22.715633383 and -22.715633383.


Subproblem 1
x + 24 = 22.715633383

Simplifying
x + 24 = 22.715633383

Reorder the terms:
24 + x = 22.715633383

Solving
24 + x = 22.715633383

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = 22.715633383 + -24

Combine like terms: 24 + -24 = 0
0 + x = 22.715633383 + -24
x = 22.715633383 + -24

Combine like terms: 22.715633383 + -24 = -1.284366617
x = -1.284366617

Simplifying
x = -1.284366617


Subproblem 2
x + 24 = -22.715633383

Simplifying
x + 24 = -22.715633383

Reorder the terms:
24 + x = -22.715633383

Solving
24 + x = -22.715633383

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = -22.715633383 + -24

Combine like terms: 24 + -24 = 0
0 + x = -22.715633383 + -24
x = -22.715633383 + -24

Combine like terms: -22.715633383 + -24 = -46.715633383
x = -46.715633383

Simplifying
x = -46.715633383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.284366617, -46.715633383}

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