x^2-50x-1500=0

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Solution for x^2-50x-1500=0 equation: 


Simplifying
x2 + -50x + -1500 = 0

Reorder the terms:
-1500 + -50x + x2 = 0

Solving
-1500 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1500' to each side of the equation.
-1500 + -50x + 1500 + x2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + -50x + x2 = 0 + 1500

Combine like terms: -1500 + 1500 = 0
0 + -50x + x2 = 0 + 1500
-50x + x2 = 0 + 1500

Combine like terms: 0 + 1500 = 1500
-50x + x2 = 1500

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 = 1500 + 625

Reorder the terms:
625 + -50x + x2 = 1500 + 625

Combine like terms: 1500 + 625 = 2125
625 + -50x + x2 = 2125

Factor a perfect square on the left side:
(x + -25)(x + -25) = 2125

Calculate the square root of the right side: 46.097722286

Break this problem into two subproblems by setting 
(x + -25) equal to 46.097722286 and -46.097722286.


Subproblem 1
x + -25 = 46.097722286

Simplifying
x + -25 = 46.097722286

Reorder the terms:
-25 + x = 46.097722286

Solving
-25 + x = 46.097722286

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 = 46.097722286 + 25

Combine like terms: -25 + 25 = 0
0 + x = 46.097722286 + 25
x = 46.097722286 + 25

Combine like terms: 46.097722286 + 25 = 71.097722286
x = 71.097722286

Simplifying
x = 71.097722286


Subproblem 2
x + -25 = -46.097722286

Simplifying
x + -25 = -46.097722286

Reorder the terms:
-25 + x = -46.097722286

Solving
-25 + x = -46.097722286

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 = -46.097722286 + 25

Combine like terms: -25 + 25 = 0
0 + x = -46.097722286 + 25
x = -46.097722286 + 25

Combine like terms: -46.097722286 + 25 = -21.097722286
x = -21.097722286

Simplifying
x = -21.097722286


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {71.097722286, -21.097722286}

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