x^2+50x+512=0

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Solution for x^2+50x+512=0 equation: 


Simplifying
x2 + 50x + 512 = 0

Reorder the terms:
512 + 50x + x2 = 0

Solving
512 + 50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-512' to each side of the equation.
512 + 50x + -512 + x2 = 0 + -512

Reorder the terms:
512 + -512 + 50x + x2 = 0 + -512

Combine like terms: 512 + -512 = 0
0 + 50x + x2 = 0 + -512
50x + x2 = 0 + -512

Combine like terms: 0 + -512 = -512
50x + x2 = -512

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 = -512 + 625

Reorder the terms:
625 + 50x + x2 = -512 + 625

Combine like terms: -512 + 625 = 113
625 + 50x + x2 = 113

Factor a perfect square on the left side:
(x + 25)(x + 25) = 113

Calculate the square root of the right side: 10.630145813

Break this problem into two subproblems by setting 
(x + 25) equal to 10.630145813 and -10.630145813.


Subproblem 1
x + 25 = 10.630145813

Simplifying
x + 25 = 10.630145813

Reorder the terms:
25 + x = 10.630145813

Solving
25 + x = 10.630145813

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 = 10.630145813 + -25

Combine like terms: 25 + -25 = 0
0 + x = 10.630145813 + -25
x = 10.630145813 + -25

Combine like terms: 10.630145813 + -25 = -14.369854187
x = -14.369854187

Simplifying
x = -14.369854187


Subproblem 2
x + 25 = -10.630145813

Simplifying
x + 25 = -10.630145813

Reorder the terms:
25 + x = -10.630145813

Solving
25 + x = -10.630145813

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 = -10.630145813 + -25

Combine like terms: 25 + -25 = 0
0 + x = -10.630145813 + -25
x = -10.630145813 + -25

Combine like terms: -10.630145813 + -25 = -35.630145813
x = -35.630145813

Simplifying
x = -35.630145813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-14.369854187, -35.630145813}

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