x^2-50x-207=0

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Solution for x^2-50x-207=0 equation: 


Simplifying
x2 + -50x + -207 = 0

Reorder the terms:
-207 + -50x + x2 = 0

Solving
-207 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '207' to each side of the equation.
-207 + -50x + 207 + x2 = 0 + 207

Reorder the terms:
-207 + 207 + -50x + x2 = 0 + 207

Combine like terms: -207 + 207 = 0
0 + -50x + x2 = 0 + 207
-50x + x2 = 0 + 207

Combine like terms: 0 + 207 = 207
-50x + x2 = 207

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = 207 + 625

Reorder the terms:
625 + -50x + x2 = 207 + 625

Combine like terms: 207 + 625 = 832
625 + -50x + x2 = 832

Factor a perfect square on the left side:
(x + -25)(x + -25) = 832

Calculate the square root of the right side: 28.844410204

Break this problem into two subproblems by setting 
(x + -25) equal to 28.844410204 and -28.844410204.


Subproblem 1
x + -25 = 28.844410204

Simplifying
x + -25 = 28.844410204

Reorder the terms:
-25 + x = 28.844410204

Solving
-25 + x = 28.844410204

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = 28.844410204 + 25

Combine like terms: -25 + 25 = 0
0 + x = 28.844410204 + 25
x = 28.844410204 + 25

Combine like terms: 28.844410204 + 25 = 53.844410204
x = 53.844410204

Simplifying
x = 53.844410204


Subproblem 2
x + -25 = -28.844410204

Simplifying
x + -25 = -28.844410204

Reorder the terms:
-25 + x = -28.844410204

Solving
-25 + x = -28.844410204

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = -28.844410204 + 25

Combine like terms: -25 + 25 = 0
0 + x = -28.844410204 + 25
x = -28.844410204 + 25

Combine like terms: -28.844410204 + 25 = -3.844410204
x = -3.844410204

Simplifying
x = -3.844410204


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.844410204, -3.844410204}

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