x^2+87x+48=0

Solution for x^2+87x+48=0 equation:

Simplifying
x2 + 87x + 48 = 0

Reorder the terms:
48 + 87x + x2 = 0

Solving
48 + 87x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + 87x + -48 + x2 = 0 + -48

Reorder the terms:
48 + -48 + 87x + x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + 87x + x2 = 0 + -48
87x + x2 = 0 + -48

Combine like terms: 0 + -48 = -48
87x + x2 = -48

The x term is 87x.  Take half its coefficient (43.5).
Square it (1892.25) and add it to both sides.

Add '1892.25' to each side of the equation.
87x + 1892.25 + x2 = -48 + 1892.25

Reorder the terms:
1892.25 + 87x + x2 = -48 + 1892.25

Combine like terms: -48 + 1892.25 = 1844.25
1892.25 + 87x + x2 = 1844.25

Factor a perfect square on the left side:
(x + 43.5)(x + 43.5) = 1844.25

Calculate the square root of the right side: 42.944731924

Break this problem into two subproblems by setting 
(x + 43.5) equal to 42.944731924 and -42.944731924.

Subproblem 1
x + 43.5 = 42.944731924

Simplifying
x + 43.5 = 42.944731924

Reorder the terms:
43.5 + x = 42.944731924

Solving
43.5 + x = 42.944731924

Solving for variable 'x'.

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

Add '-43.5' to each side of the equation.
43.5 + -43.5 + x = 42.944731924 + -43.5

Combine like terms: 43.5 + -43.5 = 0.0
0.0 + x = 42.944731924 + -43.5
x = 42.944731924 + -43.5

Combine like terms: 42.944731924 + -43.5 = -0.555268076
x = -0.555268076

Simplifying
x = -0.555268076

Subproblem 2
x + 43.5 = -42.944731924

Simplifying
x + 43.5 = -42.944731924

Reorder the terms:
43.5 + x = -42.944731924

Solving
43.5 + x = -42.944731924

Solving for variable 'x'.

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

Add '-43.5' to each side of the equation.
43.5 + -43.5 + x = -42.944731924 + -43.5

Combine like terms: 43.5 + -43.5 = 0.0
0.0 + x = -42.944731924 + -43.5
x = -42.944731924 + -43.5

Combine like terms: -42.944731924 + -43.5 = -86.444731924
x = -86.444731924

Simplifying
x = -86.444731924

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.555268076, -86.444731924}