x^2-160x-5500=0

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Solution for x^2-160x-5500=0 equation:


Simplifying
x2 + -160x + -5500 = 0

Reorder the terms:
-5500 + -160x + x2 = 0

Solving
-5500 + -160x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5500' to each side of the equation.
-5500 + -160x + 5500 + x2 = 0 + 5500

Reorder the terms:
-5500 + 5500 + -160x + x2 = 0 + 5500

Combine like terms: -5500 + 5500 = 0
0 + -160x + x2 = 0 + 5500
-160x + x2 = 0 + 5500

Combine like terms: 0 + 5500 = 5500
-160x + x2 = 5500

The x term is -160x.  Take half its coefficient (-80).
Square it (6400) and add it to both sides.

Add '6400' to each side of the equation.
-160x + 6400 + x2 = 5500 + 6400

Reorder the terms:
6400 + -160x + x2 = 5500 + 6400

Combine like terms: 5500 + 6400 = 11900
6400 + -160x + x2 = 11900

Factor a perfect square on the left side:
(x + -80)(x + -80) = 11900

Calculate the square root of the right side: 109.087121146

Break this problem into two subproblems by setting 
(x + -80) equal to 109.087121146 and -109.087121146.

Subproblem 1

x + -80 = 109.087121146 Simplifying x + -80 = 109.087121146 Reorder the terms: -80 + x = 109.087121146 Solving -80 + x = 109.087121146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 109.087121146 + 80 Combine like terms: -80 + 80 = 0 0 + x = 109.087121146 + 80 x = 109.087121146 + 80 Combine like terms: 109.087121146 + 80 = 189.087121146 x = 189.087121146 Simplifying x = 189.087121146

Subproblem 2

x + -80 = -109.087121146 Simplifying x + -80 = -109.087121146 Reorder the terms: -80 + x = -109.087121146 Solving -80 + x = -109.087121146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -109.087121146 + 80 Combine like terms: -80 + 80 = 0 0 + x = -109.087121146 + 80 x = -109.087121146 + 80 Combine like terms: -109.087121146 + 80 = -29.087121146 x = -29.087121146 Simplifying x = -29.087121146

Solution

The solution to the problem is based on the solutions from the subproblems. x = {189.087121146, -29.087121146}

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