x^2-4x+5=9

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Solution for x^2-4x+5=9 equation: 


Simplifying
x2 + -4x + 5 = 9

Reorder the terms:
5 + -4x + x2 = 9

Solving
5 + -4x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
5 + -9 + -4x + x2 = 9 + -9

Combine like terms: 5 + -9 = -4
-4 + -4x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-4 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -4x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -4x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -4x + x2 = 0 + 4
-4x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-4x + x2 = 4

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 4 + 4

Reorder the terms:
4 + -4x + x2 = 4 + 4

Combine like terms: 4 + 4 = 8
4 + -4x + x2 = 8

Factor a perfect square on the left side:
(x + -2)(x + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -2 = 2.828427125

Simplifying
x + -2 = 2.828427125

Reorder the terms:
-2 + x = 2.828427125

Solving
-2 + x = 2.828427125

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.828427125 + 2
x = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
x = 4.828427125

Simplifying
x = 4.828427125


Subproblem 2
x + -2 = -2.828427125

Simplifying
x + -2 = -2.828427125

Reorder the terms:
-2 + x = -2.828427125

Solving
-2 + x = -2.828427125

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.828427125 + 2
x = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
x = -0.828427125

Simplifying
x = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.828427125, -0.828427125}

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