X^2-45X+10=0

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Solution for X^2-45X+10=0 equation: 


Simplifying
X2 + -45X + 10 = 0

Reorder the terms:
10 + -45X + X2 = 0

Solving
10 + -45X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -45X + -10 + X2 = 0 + -10

Reorder the terms:
10 + -10 + -45X + X2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -45X + X2 = 0 + -10
-45X + X2 = 0 + -10

Combine like terms: 0 + -10 = -10
-45X + X2 = -10

The X term is -45X.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45X + 506.25 + X2 = -10 + 506.25

Reorder the terms:
506.25 + -45X + X2 = -10 + 506.25

Combine like terms: -10 + 506.25 = 496.25
506.25 + -45X + X2 = 496.25

Factor a perfect square on the left side:
(X + -22.5)(X + -22.5) = 496.25

Calculate the square root of the right side: 22.27666941

Break this problem into two subproblems by setting 
(X + -22.5) equal to 22.27666941 and -22.27666941.


Subproblem 1
X + -22.5 = 22.27666941

Simplifying
X + -22.5 = 22.27666941

Reorder the terms:
-22.5 + X = 22.27666941

Solving
-22.5 + X = 22.27666941

Solving for variable 'X'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + X = 22.27666941 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + X = 22.27666941 + 22.5
X = 22.27666941 + 22.5

Combine like terms: 22.27666941 + 22.5 = 44.77666941
X = 44.77666941

Simplifying
X = 44.77666941


Subproblem 2
X + -22.5 = -22.27666941

Simplifying
X + -22.5 = -22.27666941

Reorder the terms:
-22.5 + X = -22.27666941

Solving
-22.5 + X = -22.27666941

Solving for variable 'X'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + X = -22.27666941 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + X = -22.27666941 + 22.5
X = -22.27666941 + 22.5

Combine like terms: -22.27666941 + 22.5 = 0.22333059
X = 0.22333059

Simplifying
X = 0.22333059


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {44.77666941, 0.22333059}

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