x^2-4x=121

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Solution for x^2-4x=121 equation: 


Simplifying
x2 + -4x = 121

Reorder the terms:
-4x + x2 = 121

Solving
-4x + x2 = 121

Solving for variable 'x'.

Reorder the terms:
-121 + -4x + x2 = 121 + -121

Combine like terms: 121 + -121 = 0
-121 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + -4x + 121 + x2 = 0 + 121

Reorder the terms:
-121 + 121 + -4x + x2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + -4x + x2 = 0 + 121
-4x + x2 = 0 + 121

Combine like terms: 0 + 121 = 121
-4x + x2 = 121

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 = 121 + 4

Reorder the terms:
4 + -4x + x2 = 121 + 4

Combine like terms: 121 + 4 = 125
4 + -4x + x2 = 125

Factor a perfect square on the left side:
(x + -2)(x + -2) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + -2) equal to 11.180339887 and -11.180339887.


Subproblem 1
x + -2 = 11.180339887

Simplifying
x + -2 = 11.180339887

Reorder the terms:
-2 + x = 11.180339887

Solving
-2 + x = 11.180339887

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 = 11.180339887 + 2

Combine like terms: -2 + 2 = 0
0 + x = 11.180339887 + 2
x = 11.180339887 + 2

Combine like terms: 11.180339887 + 2 = 13.180339887
x = 13.180339887

Simplifying
x = 13.180339887


Subproblem 2
x + -2 = -11.180339887

Simplifying
x + -2 = -11.180339887

Reorder the terms:
-2 + x = -11.180339887

Solving
-2 + x = -11.180339887

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 = -11.180339887 + 2

Combine like terms: -2 + 2 = 0
0 + x = -11.180339887 + 2
x = -11.180339887 + 2

Combine like terms: -11.180339887 + 2 = -9.180339887
x = -9.180339887

Simplifying
x = -9.180339887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.180339887, -9.180339887}

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