x^2-50x-47=0

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Solution for x^2-50x-47=0 equation: 


Simplifying
x2 + -50x + -47 = 0

Reorder the terms:
-47 + -50x + x2 = 0

Solving
-47 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -50x + 47 + x2 = 0 + 47

Reorder the terms:
-47 + 47 + -50x + x2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -50x + x2 = 0 + 47
-50x + x2 = 0 + 47

Combine like terms: 0 + 47 = 47
-50x + x2 = 47

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 = 47 + 625

Reorder the terms:
625 + -50x + x2 = 47 + 625

Combine like terms: 47 + 625 = 672
625 + -50x + x2 = 672

Factor a perfect square on the left side:
(x + -25)(x + -25) = 672

Calculate the square root of the right side: 25.922962794

Break this problem into two subproblems by setting 
(x + -25) equal to 25.922962794 and -25.922962794.


Subproblem 1
x + -25 = 25.922962794

Simplifying
x + -25 = 25.922962794

Reorder the terms:
-25 + x = 25.922962794

Solving
-25 + x = 25.922962794

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 = 25.922962794 + 25

Combine like terms: -25 + 25 = 0
0 + x = 25.922962794 + 25
x = 25.922962794 + 25

Combine like terms: 25.922962794 + 25 = 50.922962794
x = 50.922962794

Simplifying
x = 50.922962794


Subproblem 2
x + -25 = -25.922962794

Simplifying
x + -25 = -25.922962794

Reorder the terms:
-25 + x = -25.922962794

Solving
-25 + x = -25.922962794

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 = -25.922962794 + 25

Combine like terms: -25 + 25 = 0
0 + x = -25.922962794 + 25
x = -25.922962794 + 25

Combine like terms: -25.922962794 + 25 = -0.922962794
x = -0.922962794

Simplifying
x = -0.922962794


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.922962794, -0.922962794}

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