x^2+55x-11000=0

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Solution for x^2+55x-11000=0 equation:


Simplifying
x2 + 55x + -11000 = 0

Reorder the terms:
-11000 + 55x + x2 = 0

Solving
-11000 + 55x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11000' to each side of the equation.
-11000 + 55x + 11000 + x2 = 0 + 11000

Reorder the terms:
-11000 + 11000 + 55x + x2 = 0 + 11000

Combine like terms: -11000 + 11000 = 0
0 + 55x + x2 = 0 + 11000
55x + x2 = 0 + 11000

Combine like terms: 0 + 11000 = 11000
55x + x2 = 11000

The x term is 55x.  Take half its coefficient (27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
55x + 756.25 + x2 = 11000 + 756.25

Reorder the terms:
756.25 + 55x + x2 = 11000 + 756.25

Combine like terms: 11000 + 756.25 = 11756.25
756.25 + 55x + x2 = 11756.25

Factor a perfect square on the left side:
(x + 27.5)(x + 27.5) = 11756.25

Calculate the square root of the right side: 108.426242211

Break this problem into two subproblems by setting 
(x + 27.5) equal to 108.426242211 and -108.426242211.

Subproblem 1

x + 27.5 = 108.426242211 Simplifying x + 27.5 = 108.426242211 Reorder the terms: 27.5 + x = 108.426242211 Solving 27.5 + x = 108.426242211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 108.426242211 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 108.426242211 + -27.5 x = 108.426242211 + -27.5 Combine like terms: 108.426242211 + -27.5 = 80.926242211 x = 80.926242211 Simplifying x = 80.926242211

Subproblem 2

x + 27.5 = -108.426242211 Simplifying x + 27.5 = -108.426242211 Reorder the terms: 27.5 + x = -108.426242211 Solving 27.5 + x = -108.426242211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -108.426242211 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -108.426242211 + -27.5 x = -108.426242211 + -27.5 Combine like terms: -108.426242211 + -27.5 = -135.926242211 x = -135.926242211 Simplifying x = -135.926242211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {80.926242211, -135.926242211}

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