x^2-21x-50=0

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Solution for x^2-21x-50=0 equation: 


Simplifying
x2 + -21x + -50 = 0

Reorder the terms:
-50 + -21x + x2 = 0

Solving
-50 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -21x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -21x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -21x + x2 = 0 + 50
-21x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-21x + x2 = 50

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = 50 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 50 + 110.25

Combine like terms: 50 + 110.25 = 160.25
110.25 + -21x + x2 = 160.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 160.25

Calculate the square root of the right side: 12.658988901

Break this problem into two subproblems by setting 
(x + -10.5) equal to 12.658988901 and -12.658988901.


Subproblem 1
x + -10.5 = 12.658988901

Simplifying
x + -10.5 = 12.658988901

Reorder the terms:
-10.5 + x = 12.658988901

Solving
-10.5 + x = 12.658988901

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 12.658988901 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 12.658988901 + 10.5
x = 12.658988901 + 10.5

Combine like terms: 12.658988901 + 10.5 = 23.158988901
x = 23.158988901

Simplifying
x = 23.158988901


Subproblem 2
x + -10.5 = -12.658988901

Simplifying
x + -10.5 = -12.658988901

Reorder the terms:
-10.5 + x = -12.658988901

Solving
-10.5 + x = -12.658988901

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -12.658988901 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -12.658988901 + 10.5
x = -12.658988901 + 10.5

Combine like terms: -12.658988901 + 10.5 = -2.158988901
x = -2.158988901

Simplifying
x = -2.158988901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.158988901, -2.158988901}

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