x^2+48x+55=0

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Solution for x^2+48x+55=0 equation: 


Simplifying
x2 + 48x + 55 = 0

Reorder the terms:
55 + 48x + x2 = 0

Solving
55 + 48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-55' to each side of the equation.
55 + 48x + -55 + x2 = 0 + -55

Reorder the terms:
55 + -55 + 48x + x2 = 0 + -55

Combine like terms: 55 + -55 = 0
0 + 48x + x2 = 0 + -55
48x + x2 = 0 + -55

Combine like terms: 0 + -55 = -55
48x + x2 = -55

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 = -55 + 576

Reorder the terms:
576 + 48x + x2 = -55 + 576

Combine like terms: -55 + 576 = 521
576 + 48x + x2 = 521

Factor a perfect square on the left side:
(x + 24)(x + 24) = 521

Calculate the square root of the right side: 22.825424421

Break this problem into two subproblems by setting 
(x + 24) equal to 22.825424421 and -22.825424421.


Subproblem 1
x + 24 = 22.825424421

Simplifying
x + 24 = 22.825424421

Reorder the terms:
24 + x = 22.825424421

Solving
24 + x = 22.825424421

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 = 22.825424421 + -24

Combine like terms: 24 + -24 = 0
0 + x = 22.825424421 + -24
x = 22.825424421 + -24

Combine like terms: 22.825424421 + -24 = -1.174575579
x = -1.174575579

Simplifying
x = -1.174575579


Subproblem 2
x + 24 = -22.825424421

Simplifying
x + 24 = -22.825424421

Reorder the terms:
24 + x = -22.825424421

Solving
24 + x = -22.825424421

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 = -22.825424421 + -24

Combine like terms: 24 + -24 = 0
0 + x = -22.825424421 + -24
x = -22.825424421 + -24

Combine like terms: -22.825424421 + -24 = -46.825424421
x = -46.825424421

Simplifying
x = -46.825424421


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.174575579, -46.825424421}

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