x^2-44x+225=0

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Solution for x^2-44x+225=0 equation: 


Simplifying
x2 + -44x + 225 = 0

Reorder the terms:
225 + -44x + x2 = 0

Solving
225 + -44x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-225' to each side of the equation.
225 + -44x + -225 + x2 = 0 + -225

Reorder the terms:
225 + -225 + -44x + x2 = 0 + -225

Combine like terms: 225 + -225 = 0
0 + -44x + x2 = 0 + -225
-44x + x2 = 0 + -225

Combine like terms: 0 + -225 = -225
-44x + x2 = -225

The x term is -44x.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44x + 484 + x2 = -225 + 484

Reorder the terms:
484 + -44x + x2 = -225 + 484

Combine like terms: -225 + 484 = 259
484 + -44x + x2 = 259

Factor a perfect square on the left side:
(x + -22)(x + -22) = 259

Calculate the square root of the right side: 16.093476939

Break this problem into two subproblems by setting 
(x + -22) equal to 16.093476939 and -16.093476939.


Subproblem 1
x + -22 = 16.093476939

Simplifying
x + -22 = 16.093476939

Reorder the terms:
-22 + x = 16.093476939

Solving
-22 + x = 16.093476939

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = 16.093476939 + 22

Combine like terms: -22 + 22 = 0
0 + x = 16.093476939 + 22
x = 16.093476939 + 22

Combine like terms: 16.093476939 + 22 = 38.093476939
x = 38.093476939

Simplifying
x = 38.093476939


Subproblem 2
x + -22 = -16.093476939

Simplifying
x + -22 = -16.093476939

Reorder the terms:
-22 + x = -16.093476939

Solving
-22 + x = -16.093476939

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = -16.093476939 + 22

Combine like terms: -22 + 22 = 0
0 + x = -16.093476939 + 22
x = -16.093476939 + 22

Combine like terms: -16.093476939 + 22 = 5.906523061
x = 5.906523061

Simplifying
x = 5.906523061


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.093476939, 5.906523061}

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