x^2-4x-490=0

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Solution for x^2-4x-490=0 equation: 


Simplifying
x2 + -4x + -490 = 0

Reorder the terms:
-490 + -4x + x2 = 0

Solving
-490 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '490' to each side of the equation.
-490 + -4x + 490 + x2 = 0 + 490

Reorder the terms:
-490 + 490 + -4x + x2 = 0 + 490

Combine like terms: -490 + 490 = 0
0 + -4x + x2 = 0 + 490
-4x + x2 = 0 + 490

Combine like terms: 0 + 490 = 490
-4x + x2 = 490

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 490 + 4

Reorder the terms:
4 + -4x + x2 = 490 + 4

Combine like terms: 490 + 4 = 494
4 + -4x + x2 = 494

Factor a perfect square on the left side:
(x + -2)(x + -2) = 494

Calculate the square root of the right side: 22.226110771

Break this problem into two subproblems by setting 
(x + -2) equal to 22.226110771 and -22.226110771.


Subproblem 1
x + -2 = 22.226110771

Simplifying
x + -2 = 22.226110771

Reorder the terms:
-2 + x = 22.226110771

Solving
-2 + x = 22.226110771

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 22.226110771 + 2

Combine like terms: -2 + 2 = 0
0 + x = 22.226110771 + 2
x = 22.226110771 + 2

Combine like terms: 22.226110771 + 2 = 24.226110771
x = 24.226110771

Simplifying
x = 24.226110771


Subproblem 2
x + -2 = -22.226110771

Simplifying
x + -2 = -22.226110771

Reorder the terms:
-2 + x = -22.226110771

Solving
-2 + x = -22.226110771

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -22.226110771 + 2

Combine like terms: -2 + 2 = 0
0 + x = -22.226110771 + 2
x = -22.226110771 + 2

Combine like terms: -22.226110771 + 2 = -20.226110771
x = -20.226110771

Simplifying
x = -20.226110771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.226110771, -20.226110771}

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