x^2+20x+48=0

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Solution for x^2+20x+48=0 equation: 


Simplifying
x2 + 20x + 48 = 0

Reorder the terms:
48 + 20x + x2 = 0

Solving
48 + 20x + 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 + 20x + -48 + x2 = 0 + -48

Reorder the terms:
48 + -48 + 20x + x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + 20x + x2 = 0 + -48
20x + x2 = 0 + -48

Combine like terms: 0 + -48 = -48
20x + x2 = -48

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -48 + 100

Reorder the terms:
100 + 20x + x2 = -48 + 100

Combine like terms: -48 + 100 = 52
100 + 20x + x2 = 52

Factor a perfect square on the left side:
(x + 10)(x + 10) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 10) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + 10 = 7.211102551

Simplifying
x + 10 = 7.211102551

Reorder the terms:
10 + x = 7.211102551

Solving
10 + x = 7.211102551

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 7.211102551 + -10

Combine like terms: 10 + -10 = 0
0 + x = 7.211102551 + -10
x = 7.211102551 + -10

Combine like terms: 7.211102551 + -10 = -2.788897449
x = -2.788897449

Simplifying
x = -2.788897449


Subproblem 2
x + 10 = -7.211102551

Simplifying
x + 10 = -7.211102551

Reorder the terms:
10 + x = -7.211102551

Solving
10 + x = -7.211102551

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -7.211102551 + -10

Combine like terms: 10 + -10 = 0
0 + x = -7.211102551 + -10
x = -7.211102551 + -10

Combine like terms: -7.211102551 + -10 = -17.211102551
x = -17.211102551

Simplifying
x = -17.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.788897449, -17.211102551}

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