x^2+47x+56=0

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Solution for x^2+47x+56=0 equation: 


Simplifying
x2 + 47x + 56 = 0

Reorder the terms:
56 + 47x + x2 = 0

Solving
56 + 47x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + 47x + -56 + x2 = 0 + -56

Reorder the terms:
56 + -56 + 47x + x2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + 47x + x2 = 0 + -56
47x + x2 = 0 + -56

Combine like terms: 0 + -56 = -56
47x + x2 = -56

The x term is 47x.  Take half its coefficient (23.5).
Square it (552.25) and add it to both sides.

Add '552.25' to each side of the equation.
47x + 552.25 + x2 = -56 + 552.25

Reorder the terms:
552.25 + 47x + x2 = -56 + 552.25

Combine like terms: -56 + 552.25 = 496.25
552.25 + 47x + x2 = 496.25

Factor a perfect square on the left side:
(x + 23.5)(x + 23.5) = 496.25

Calculate the square root of the right side: 22.27666941

Break this problem into two subproblems by setting 
(x + 23.5) equal to 22.27666941 and -22.27666941.


Subproblem 1
x + 23.5 = 22.27666941

Simplifying
x + 23.5 = 22.27666941

Reorder the terms:
23.5 + x = 22.27666941

Solving
23.5 + x = 22.27666941

Solving for variable 'x'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + x = 22.27666941 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = 22.27666941 + -23.5
x = 22.27666941 + -23.5

Combine like terms: 22.27666941 + -23.5 = -1.22333059
x = -1.22333059

Simplifying
x = -1.22333059


Subproblem 2
x + 23.5 = -22.27666941

Simplifying
x + 23.5 = -22.27666941

Reorder the terms:
23.5 + x = -22.27666941

Solving
23.5 + x = -22.27666941

Solving for variable 'x'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + x = -22.27666941 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = -22.27666941 + -23.5
x = -22.27666941 + -23.5

Combine like terms: -22.27666941 + -23.5 = -45.77666941
x = -45.77666941

Simplifying
x = -45.77666941


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.22333059, -45.77666941}

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