x^2-32x+200=0

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Solution for x^2-32x+200=0 equation: 


Simplifying
x2 + -32x + 200 = 0

Reorder the terms:
200 + -32x + x2 = 0

Solving
200 + -32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -32x + -200 + x2 = 0 + -200

Reorder the terms:
200 + -200 + -32x + x2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -32x + x2 = 0 + -200
-32x + x2 = 0 + -200

Combine like terms: 0 + -200 = -200
-32x + x2 = -200

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = -200 + 256

Reorder the terms:
256 + -32x + x2 = -200 + 256

Combine like terms: -200 + 256 = 56
256 + -32x + x2 = 56

Factor a perfect square on the left side:
(x + -16)(x + -16) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + -16) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + -16 = 7.483314774

Simplifying
x + -16 = 7.483314774

Reorder the terms:
-16 + x = 7.483314774

Solving
-16 + x = 7.483314774

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '16' to each side of the equation.
-16 + 16 + x = 7.483314774 + 16

Combine like terms: -16 + 16 = 0
0 + x = 7.483314774 + 16
x = 7.483314774 + 16

Combine like terms: 7.483314774 + 16 = 23.483314774
x = 23.483314774

Simplifying
x = 23.483314774


Subproblem 2
x + -16 = -7.483314774

Simplifying
x + -16 = -7.483314774

Reorder the terms:
-16 + x = -7.483314774

Solving
-16 + x = -7.483314774

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '16' to each side of the equation.
-16 + 16 + x = -7.483314774 + 16

Combine like terms: -16 + 16 = 0
0 + x = -7.483314774 + 16
x = -7.483314774 + 16

Combine like terms: -7.483314774 + 16 = 8.516685226
x = 8.516685226

Simplifying
x = 8.516685226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.483314774, 8.516685226}

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