x^2+84x+128=0

Solution for x^2+84x+128=0 equation:

Simplifying
x2 + 84x + 128 = 0

Reorder the terms:
128 + 84x + x2 = 0

Solving
128 + 84x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-128' to each side of the equation.
128 + 84x + -128 + x2 = 0 + -128

Reorder the terms:
128 + -128 + 84x + x2 = 0 + -128

Combine like terms: 128 + -128 = 0
0 + 84x + x2 = 0 + -128
84x + x2 = 0 + -128

Combine like terms: 0 + -128 = -128
84x + x2 = -128

The x term is 84x.  Take half its coefficient (42).
Square it (1764) and add it to both sides.

Add '1764' to each side of the equation.
84x + 1764 + x2 = -128 + 1764

Reorder the terms:
1764 + 84x + x2 = -128 + 1764

Combine like terms: -128 + 1764 = 1636
1764 + 84x + x2 = 1636

Factor a perfect square on the left side:
(x + 42)(x + 42) = 1636

Calculate the square root of the right side: 40.447496832

Break this problem into two subproblems by setting 
(x + 42) equal to 40.447496832 and -40.447496832.

Subproblem 1
x + 42 = 40.447496832

Simplifying
x + 42 = 40.447496832

Reorder the terms:
42 + x = 40.447496832

Solving
42 + x = 40.447496832

Solving for variable 'x'.

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

Add '-42' to each side of the equation.
42 + -42 + x = 40.447496832 + -42

Combine like terms: 42 + -42 = 0
0 + x = 40.447496832 + -42
x = 40.447496832 + -42

Combine like terms: 40.447496832 + -42 = -1.552503168
x = -1.552503168

Simplifying
x = -1.552503168

Subproblem 2
x + 42 = -40.447496832

Simplifying
x + 42 = -40.447496832

Reorder the terms:
42 + x = -40.447496832

Solving
42 + x = -40.447496832

Solving for variable 'x'.

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

Add '-42' to each side of the equation.
42 + -42 + x = -40.447496832 + -42

Combine like terms: 42 + -42 = 0
0 + x = -40.447496832 + -42
x = -40.447496832 + -42

Combine like terms: -40.447496832 + -42 = -82.447496832
x = -82.447496832

Simplifying
x = -82.447496832

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.552503168, -82.447496832}