x^2+50x-60000=0

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Solution for x^2+50x-60000=0 equation: 


Simplifying
x2 + 50x + -60000 = 0

Reorder the terms:
-60000 + 50x + x2 = 0

Solving
-60000 + 50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60000' to each side of the equation.
-60000 + 50x + 60000 + x2 = 0 + 60000

Reorder the terms:
-60000 + 60000 + 50x + x2 = 0 + 60000

Combine like terms: -60000 + 60000 = 0
0 + 50x + x2 = 0 + 60000
50x + x2 = 0 + 60000

Combine like terms: 0 + 60000 = 60000
50x + x2 = 60000

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 = 60000 + 625

Reorder the terms:
625 + 50x + x2 = 60000 + 625

Combine like terms: 60000 + 625 = 60625
625 + 50x + x2 = 60625

Factor a perfect square on the left side:
(x + 25)(x + 25) = 60625

Calculate the square root of the right side: 246.221445045

Break this problem into two subproblems by setting 
(x + 25) equal to 246.221445045 and -246.221445045.


Subproblem 1
x + 25 = 246.221445045

Simplifying
x + 25 = 246.221445045

Reorder the terms:
25 + x = 246.221445045

Solving
25 + x = 246.221445045

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 = 246.221445045 + -25

Combine like terms: 25 + -25 = 0
0 + x = 246.221445045 + -25
x = 246.221445045 + -25

Combine like terms: 246.221445045 + -25 = 221.221445045
x = 221.221445045

Simplifying
x = 221.221445045


Subproblem 2
x + 25 = -246.221445045

Simplifying
x + 25 = -246.221445045

Reorder the terms:
25 + x = -246.221445045

Solving
25 + x = -246.221445045

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 = -246.221445045 + -25

Combine like terms: 25 + -25 = 0
0 + x = -246.221445045 + -25
x = -246.221445045 + -25

Combine like terms: -246.221445045 + -25 = -271.221445045
x = -271.221445045

Simplifying
x = -271.221445045


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {221.221445045, -271.221445045}

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