x^2+56x+612=0

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Solution for x^2+56x+612=0 equation: 


Simplifying
x2 + 56x + 612 = 0

Reorder the terms:
612 + 56x + x2 = 0

Solving
612 + 56x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-612' to each side of the equation.
612 + 56x + -612 + x2 = 0 + -612

Reorder the terms:
612 + -612 + 56x + x2 = 0 + -612

Combine like terms: 612 + -612 = 0
0 + 56x + x2 = 0 + -612
56x + x2 = 0 + -612

Combine like terms: 0 + -612 = -612
56x + x2 = -612

The x term is 56x.  Take half its coefficient (28).
Square it (784) and add it to both sides.

Add '784' to each side of the equation.
56x + 784 + x2 = -612 + 784

Reorder the terms:
784 + 56x + x2 = -612 + 784

Combine like terms: -612 + 784 = 172
784 + 56x + x2 = 172

Factor a perfect square on the left side:
(x + 28)(x + 28) = 172

Calculate the square root of the right side: 13.114877049

Break this problem into two subproblems by setting 
(x + 28) equal to 13.114877049 and -13.114877049.


Subproblem 1
x + 28 = 13.114877049

Simplifying
x + 28 = 13.114877049

Reorder the terms:
28 + x = 13.114877049

Solving
28 + x = 13.114877049

Solving for variable 'x'.

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

Add '-28' to each side of the equation.
28 + -28 + x = 13.114877049 + -28

Combine like terms: 28 + -28 = 0
0 + x = 13.114877049 + -28
x = 13.114877049 + -28

Combine like terms: 13.114877049 + -28 = -14.885122951
x = -14.885122951

Simplifying
x = -14.885122951


Subproblem 2
x + 28 = -13.114877049

Simplifying
x + 28 = -13.114877049

Reorder the terms:
28 + x = -13.114877049

Solving
28 + x = -13.114877049

Solving for variable 'x'.

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

Add '-28' to each side of the equation.
28 + -28 + x = -13.114877049 + -28

Combine like terms: 28 + -28 = 0
0 + x = -13.114877049 + -28
x = -13.114877049 + -28

Combine like terms: -13.114877049 + -28 = -41.114877049
x = -41.114877049

Simplifying
x = -41.114877049


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-14.885122951, -41.114877049}

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