x^2-4x-245=0

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Solution for x^2-4x-245=0 equation: 


Simplifying
x2 + -4x + -245 = 0

Reorder the terms:
-245 + -4x + x2 = 0

Solving
-245 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '245' to each side of the equation.
-245 + -4x + 245 + x2 = 0 + 245

Reorder the terms:
-245 + 245 + -4x + x2 = 0 + 245

Combine like terms: -245 + 245 = 0
0 + -4x + x2 = 0 + 245
-4x + x2 = 0 + 245

Combine like terms: 0 + 245 = 245
-4x + x2 = 245

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 = 245 + 4

Reorder the terms:
4 + -4x + x2 = 245 + 4

Combine like terms: 245 + 4 = 249
4 + -4x + x2 = 249

Factor a perfect square on the left side:
(x + -2)(x + -2) = 249

Calculate the square root of the right side: 15.779733838

Break this problem into two subproblems by setting 
(x + -2) equal to 15.779733838 and -15.779733838.


Subproblem 1
x + -2 = 15.779733838

Simplifying
x + -2 = 15.779733838

Reorder the terms:
-2 + x = 15.779733838

Solving
-2 + x = 15.779733838

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 = 15.779733838 + 2

Combine like terms: -2 + 2 = 0
0 + x = 15.779733838 + 2
x = 15.779733838 + 2

Combine like terms: 15.779733838 + 2 = 17.779733838
x = 17.779733838

Simplifying
x = 17.779733838


Subproblem 2
x + -2 = -15.779733838

Simplifying
x + -2 = -15.779733838

Reorder the terms:
-2 + x = -15.779733838

Solving
-2 + x = -15.779733838

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 = -15.779733838 + 2

Combine like terms: -2 + 2 = 0
0 + x = -15.779733838 + 2
x = -15.779733838 + 2

Combine like terms: -15.779733838 + 2 = -13.779733838
x = -13.779733838

Simplifying
x = -13.779733838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.779733838, -13.779733838}

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