x^2-50x-375=0

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Solution for x^2-50x-375=0 equation:


Simplifying
x2 + -50x + -375 = 0

Reorder the terms:
-375 + -50x + x2 = 0

Solving
-375 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '375' to each side of the equation.
-375 + -50x + 375 + x2 = 0 + 375

Reorder the terms:
-375 + 375 + -50x + x2 = 0 + 375

Combine like terms: -375 + 375 = 0
0 + -50x + x2 = 0 + 375
-50x + x2 = 0 + 375

Combine like terms: 0 + 375 = 375
-50x + x2 = 375

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 = 375 + 625

Reorder the terms:
625 + -50x + x2 = 375 + 625

Combine like terms: 375 + 625 = 1000
625 + -50x + x2 = 1000

Factor a perfect square on the left side:
(x + -25)(x + -25) = 1000

Calculate the square root of the right side: 31.622776602

Break this problem into two subproblems by setting 
(x + -25) equal to 31.622776602 and -31.622776602.


Subproblem 1
x + -25 = 31.622776602

Simplifying
x + -25 = 31.622776602

Reorder the terms:
-25 + x = 31.622776602

Solving
-25 + x = 31.622776602

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 = 31.622776602 + 25

Combine like terms: -25 + 25 = 0
0 + x = 31.622776602 + 25
x = 31.622776602 + 25

Combine like terms: 31.622776602 + 25 = 56.622776602
x = 56.622776602

Simplifying
x = 56.622776602


Subproblem 2
x + -25 = -31.622776602

Simplifying
x + -25 = -31.622776602

Reorder the terms:
-25 + x = -31.622776602

Solving
-25 + x = -31.622776602

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 = -31.622776602 + 25

Combine like terms: -25 + 25 = 0
0 + x = -31.622776602 + 25
x = -31.622776602 + 25

Combine like terms: -31.622776602 + 25 = -6.622776602
x = -6.622776602

Simplifying
x = -6.622776602


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.622776602, -6.622776602}

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