x^2-50x+305=0

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Solution for x^2-50x+305=0 equation: 


Simplifying
x2 + -50x + 305 = 0

Reorder the terms:
305 + -50x + x2 = 0

Solving
305 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-305' to each side of the equation.
305 + -50x + -305 + x2 = 0 + -305

Reorder the terms:
305 + -305 + -50x + x2 = 0 + -305

Combine like terms: 305 + -305 = 0
0 + -50x + x2 = 0 + -305
-50x + x2 = 0 + -305

Combine like terms: 0 + -305 = -305
-50x + x2 = -305

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 = -305 + 625

Reorder the terms:
625 + -50x + x2 = -305 + 625

Combine like terms: -305 + 625 = 320
625 + -50x + x2 = 320

Factor a perfect square on the left side:
(x + -25)(x + -25) = 320

Calculate the square root of the right side: 17.88854382

Break this problem into two subproblems by setting 
(x + -25) equal to 17.88854382 and -17.88854382.


Subproblem 1
x + -25 = 17.88854382

Simplifying
x + -25 = 17.88854382

Reorder the terms:
-25 + x = 17.88854382

Solving
-25 + x = 17.88854382

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 = 17.88854382 + 25

Combine like terms: -25 + 25 = 0
0 + x = 17.88854382 + 25
x = 17.88854382 + 25

Combine like terms: 17.88854382 + 25 = 42.88854382
x = 42.88854382

Simplifying
x = 42.88854382


Subproblem 2
x + -25 = -17.88854382

Simplifying
x + -25 = -17.88854382

Reorder the terms:
-25 + x = -17.88854382

Solving
-25 + x = -17.88854382

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 = -17.88854382 + 25

Combine like terms: -25 + 25 = 0
0 + x = -17.88854382 + 25
x = -17.88854382 + 25

Combine like terms: -17.88854382 + 25 = 7.11145618
x = 7.11145618

Simplifying
x = 7.11145618


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.88854382, 7.11145618}

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