-x^2+9x-2=0

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Solution for -x^2+9x-2=0 equation: 


Simplifying
-1x2 + 9x + -2 = 0

Reorder the terms:
-2 + 9x + -1x2 = 0

Solving
-2 + 9x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -9x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -9x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -9x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9x + x2 = 0 + -2
-9x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-9x + x2 = -2

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -2 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -2 + 20.25

Combine like terms: -2 + 20.25 = 18.25
20.25 + -9x + x2 = 18.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + -4.5 = 4.272001873

Simplifying
x + -4.5 = 4.272001873

Reorder the terms:
-4.5 + x = 4.272001873

Solving
-4.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.272001873 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.272001873 + 4.5
x = 4.272001873 + 4.5

Combine like terms: 4.272001873 + 4.5 = 8.772001873
x = 8.772001873

Simplifying
x = 8.772001873


Subproblem 2
x + -4.5 = -4.272001873

Simplifying
x + -4.5 = -4.272001873

Reorder the terms:
-4.5 + x = -4.272001873

Solving
-4.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.272001873 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.272001873 + 4.5
x = -4.272001873 + 4.5

Combine like terms: -4.272001873 + 4.5 = 0.227998127
x = 0.227998127

Simplifying
x = 0.227998127


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.772001873, 0.227998127}

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