x^2-50x+312=0

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Solution for x^2-50x+312=0 equation: 


Simplifying
x2 + -50x + 312 = 0

Reorder the terms:
312 + -50x + x2 = 0

Solving
312 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-312' to each side of the equation.
312 + -50x + -312 + x2 = 0 + -312

Reorder the terms:
312 + -312 + -50x + x2 = 0 + -312

Combine like terms: 312 + -312 = 0
0 + -50x + x2 = 0 + -312
-50x + x2 = 0 + -312

Combine like terms: 0 + -312 = -312
-50x + x2 = -312

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 = -312 + 625

Reorder the terms:
625 + -50x + x2 = -312 + 625

Combine like terms: -312 + 625 = 313
625 + -50x + x2 = 313

Factor a perfect square on the left side:
(x + -25)(x + -25) = 313

Calculate the square root of the right side: 17.691806013

Break this problem into two subproblems by setting 
(x + -25) equal to 17.691806013 and -17.691806013.


Subproblem 1
x + -25 = 17.691806013

Simplifying
x + -25 = 17.691806013

Reorder the terms:
-25 + x = 17.691806013

Solving
-25 + x = 17.691806013

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 = 17.691806013 + 25

Combine like terms: -25 + 25 = 0
0 + x = 17.691806013 + 25
x = 17.691806013 + 25

Combine like terms: 17.691806013 + 25 = 42.691806013
x = 42.691806013

Simplifying
x = 42.691806013


Subproblem 2
x + -25 = -17.691806013

Simplifying
x + -25 = -17.691806013

Reorder the terms:
-25 + x = -17.691806013

Solving
-25 + x = -17.691806013

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 = -17.691806013 + 25

Combine like terms: -25 + 25 = 0
0 + x = -17.691806013 + 25
x = -17.691806013 + 25

Combine like terms: -17.691806013 + 25 = 7.308193987
x = 7.308193987

Simplifying
x = 7.308193987


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.691806013, 7.308193987}

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