x^2+56x+85=0

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Solution for x^2+56x+85=0 equation:


Simplifying
x2 + 56x + 85 = 0

Reorder the terms:
85 + 56x + x2 = 0

Solving
85 + 56x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-85' to each side of the equation.
85 + 56x + -85 + x2 = 0 + -85

Reorder the terms:
85 + -85 + 56x + x2 = 0 + -85

Combine like terms: 85 + -85 = 0
0 + 56x + x2 = 0 + -85
56x + x2 = 0 + -85

Combine like terms: 0 + -85 = -85
56x + x2 = -85

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 = -85 + 784

Reorder the terms:
784 + 56x + x2 = -85 + 784

Combine like terms: -85 + 784 = 699
784 + 56x + x2 = 699

Factor a perfect square on the left side:
(x + 28)(x + 28) = 699

Calculate the square root of the right side: 26.438608133

Break this problem into two subproblems by setting 
(x + 28) equal to 26.438608133 and -26.438608133.


Subproblem 1
x + 28 = 26.438608133

Simplifying
x + 28 = 26.438608133

Reorder the terms:
28 + x = 26.438608133

Solving
28 + x = 26.438608133

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 = 26.438608133 + -28

Combine like terms: 28 + -28 = 0
0 + x = 26.438608133 + -28
x = 26.438608133 + -28

Combine like terms: 26.438608133 + -28 = -1.561391867
x = -1.561391867

Simplifying
x = -1.561391867


Subproblem 2
x + 28 = -26.438608133

Simplifying
x + 28 = -26.438608133

Reorder the terms:
28 + x = -26.438608133

Solving
28 + x = -26.438608133

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 = -26.438608133 + -28

Combine like terms: 28 + -28 = 0
0 + x = -26.438608133 + -28
x = -26.438608133 + -28

Combine like terms: -26.438608133 + -28 = -54.438608133
x = -54.438608133

Simplifying
x = -54.438608133


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.561391867, -54.438608133}

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