x^2-124x-600=0

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Solution for x^2-124x-600=0 equation: 


Simplifying
x2 + -124x + -600 = 0

Reorder the terms:
-600 + -124x + x2 = 0

Solving
-600 + -124x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '600' to each side of the equation.
-600 + -124x + 600 + x2 = 0 + 600

Reorder the terms:
-600 + 600 + -124x + x2 = 0 + 600

Combine like terms: -600 + 600 = 0
0 + -124x + x2 = 0 + 600
-124x + x2 = 0 + 600

Combine like terms: 0 + 600 = 600
-124x + x2 = 600

The x term is -124x.  Take half its coefficient (-62).
Square it (3844) and add it to both sides.

Add '3844' to each side of the equation.
-124x + 3844 + x2 = 600 + 3844

Reorder the terms:
3844 + -124x + x2 = 600 + 3844

Combine like terms: 600 + 3844 = 4444
3844 + -124x + x2 = 4444

Factor a perfect square on the left side:
(x + -62)(x + -62) = 4444

Calculate the square root of the right side: 66.66333325

Break this problem into two subproblems by setting 
(x + -62) equal to 66.66333325 and -66.66333325.


Subproblem 1
x + -62 = 66.66333325

Simplifying
x + -62 = 66.66333325

Reorder the terms:
-62 + x = 66.66333325

Solving
-62 + x = 66.66333325

Solving for variable 'x'.

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

Add '62' to each side of the equation.
-62 + 62 + x = 66.66333325 + 62

Combine like terms: -62 + 62 = 0
0 + x = 66.66333325 + 62
x = 66.66333325 + 62

Combine like terms: 66.66333325 + 62 = 128.66333325
x = 128.66333325

Simplifying
x = 128.66333325


Subproblem 2
x + -62 = -66.66333325

Simplifying
x + -62 = -66.66333325

Reorder the terms:
-62 + x = -66.66333325

Solving
-62 + x = -66.66333325

Solving for variable 'x'.

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

Add '62' to each side of the equation.
-62 + 62 + x = -66.66333325 + 62

Combine like terms: -62 + 62 = 0
0 + x = -66.66333325 + 62
x = -66.66333325 + 62

Combine like terms: -66.66333325 + 62 = -4.66333325
x = -4.66333325

Simplifying
x = -4.66333325


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {128.66333325, -4.66333325}

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