x^2+50x+50=0

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


Simplifying
x2 + 50x + 50 = 0

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

Solving
50 + 50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -50 + 625

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

Combine like terms: -50 + 625 = 575
625 + 50x + x2 = 575

Factor a perfect square on the left side:
(x + 25)(x + 25) = 575

Calculate the square root of the right side: 23.979157617

Break this problem into two subproblems by setting 
(x + 25) equal to 23.979157617 and -23.979157617.


Subproblem 1
x + 25 = 23.979157617

Simplifying
x + 25 = 23.979157617

Reorder the terms:
25 + x = 23.979157617

Solving
25 + x = 23.979157617

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 = 23.979157617 + -25

Combine like terms: 25 + -25 = 0
0 + x = 23.979157617 + -25
x = 23.979157617 + -25

Combine like terms: 23.979157617 + -25 = -1.020842383
x = -1.020842383

Simplifying
x = -1.020842383


Subproblem 2
x + 25 = -23.979157617

Simplifying
x + 25 = -23.979157617

Reorder the terms:
25 + x = -23.979157617

Solving
25 + x = -23.979157617

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 = -23.979157617 + -25

Combine like terms: 25 + -25 = 0
0 + x = -23.979157617 + -25
x = -23.979157617 + -25

Combine like terms: -23.979157617 + -25 = -48.979157617
x = -48.979157617

Simplifying
x = -48.979157617


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.020842383, -48.979157617}

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