x^2-10x+22=0

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Solution for x^2-10x+22=0 equation: 


Simplifying
x2 + -10x + 22 = 0

Reorder the terms:
22 + -10x + x2 = 0

Solving
22 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -10x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + -10x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -10x + x2 = 0 + -22
-10x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
-10x + x2 = -22

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -22 + 25

Reorder the terms:
25 + -10x + x2 = -22 + 25

Combine like terms: -22 + 25 = 3
25 + -10x + x2 = 3

Factor a perfect square on the left side:
(x + -5)(x + -5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -5) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -5 = 1.732050808

Simplifying
x + -5 = 1.732050808

Reorder the terms:
-5 + x = 1.732050808

Solving
-5 + x = 1.732050808

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 1.732050808 + 5

Combine like terms: -5 + 5 = 0
0 + x = 1.732050808 + 5
x = 1.732050808 + 5

Combine like terms: 1.732050808 + 5 = 6.732050808
x = 6.732050808

Simplifying
x = 6.732050808


Subproblem 2
x + -5 = -1.732050808

Simplifying
x + -5 = -1.732050808

Reorder the terms:
-5 + x = -1.732050808

Solving
-5 + x = -1.732050808

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -1.732050808 + 5

Combine like terms: -5 + 5 = 0
0 + x = -1.732050808 + 5
x = -1.732050808 + 5

Combine like terms: -1.732050808 + 5 = 3.267949192
x = 3.267949192

Simplifying
x = 3.267949192


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.732050808, 3.267949192}

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