x^2-100x-24=0

Solution for x^2-100x-24=0 equation:

Simplifying
x2 + -100x + -24 = 0

Reorder the terms:
-24 + -100x + x2 = 0

Solving
-24 + -100x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -100x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -100x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -100x + x2 = 0 + 24
-100x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-100x + x2 = 24

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = 24 + 2500

Reorder the terms:
2500 + -100x + x2 = 24 + 2500

Combine like terms: 24 + 2500 = 2524
2500 + -100x + x2 = 2524

Factor a perfect square on the left side:
(x + -50)(x + -50) = 2524

Calculate the square root of the right side: 50.239426748

Break this problem into two subproblems by setting 
(x + -50) equal to 50.239426748 and -50.239426748.

Subproblem 1
x + -50 = 50.239426748

Simplifying
x + -50 = 50.239426748

Reorder the terms:
-50 + x = 50.239426748

Solving
-50 + x = 50.239426748

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = 50.239426748 + 50

Combine like terms: -50 + 50 = 0
0 + x = 50.239426748 + 50
x = 50.239426748 + 50

Combine like terms: 50.239426748 + 50 = 100.239426748
x = 100.239426748

Simplifying
x = 100.239426748

Subproblem 2
x + -50 = -50.239426748

Simplifying
x + -50 = -50.239426748

Reorder the terms:
-50 + x = -50.239426748

Solving
-50 + x = -50.239426748

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = -50.239426748 + 50

Combine like terms: -50 + 50 = 0
0 + x = -50.239426748 + 50
x = -50.239426748 + 50

Combine like terms: -50.239426748 + 50 = -0.239426748
x = -0.239426748

Simplifying
x = -0.239426748

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {100.239426748, -0.239426748}