x^2-242x-440=0

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Solution for x^2-242x-440=0 equation: 


Simplifying
x2 + -242x + -440 = 0

Reorder the terms:
-440 + -242x + x2 = 0

Solving
-440 + -242x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '440' to each side of the equation.
-440 + -242x + 440 + x2 = 0 + 440

Reorder the terms:
-440 + 440 + -242x + x2 = 0 + 440

Combine like terms: -440 + 440 = 0
0 + -242x + x2 = 0 + 440
-242x + x2 = 0 + 440

Combine like terms: 0 + 440 = 440
-242x + x2 = 440

The x term is -242x.  Take half its coefficient (-121).
Square it (14641) and add it to both sides.

Add '14641' to each side of the equation.
-242x + 14641 + x2 = 440 + 14641

Reorder the terms:
14641 + -242x + x2 = 440 + 14641

Combine like terms: 440 + 14641 = 15081
14641 + -242x + x2 = 15081

Factor a perfect square on the left side:
(x + -121)(x + -121) = 15081

Calculate the square root of the right side: 122.804723036

Break this problem into two subproblems by setting 
(x + -121) equal to 122.804723036 and -122.804723036.


Subproblem 1
x + -121 = 122.804723036

Simplifying
x + -121 = 122.804723036

Reorder the terms:
-121 + x = 122.804723036

Solving
-121 + x = 122.804723036

Solving for variable 'x'.

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

Add '121' to each side of the equation.
-121 + 121 + x = 122.804723036 + 121

Combine like terms: -121 + 121 = 0
0 + x = 122.804723036 + 121
x = 122.804723036 + 121

Combine like terms: 122.804723036 + 121 = 243.804723036
x = 243.804723036

Simplifying
x = 243.804723036


Subproblem 2
x + -121 = -122.804723036

Simplifying
x + -121 = -122.804723036

Reorder the terms:
-121 + x = -122.804723036

Solving
-121 + x = -122.804723036

Solving for variable 'x'.

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

Add '121' to each side of the equation.
-121 + 121 + x = -122.804723036 + 121

Combine like terms: -121 + 121 = 0
0 + x = -122.804723036 + 121
x = -122.804723036 + 121

Combine like terms: -122.804723036 + 121 = -1.804723036
x = -1.804723036

Simplifying
x = -1.804723036


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {243.804723036, -1.804723036}

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