x*x-4.5x+0.5=0

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Solution for x*x-4.5x+0.5=0 equation: 


Simplifying
x * x + -4.5x + 0.5 = 0

Multiply x * x
x2 + -4.5x + 0.5 = 0

Reorder the terms:
0.5 + -4.5x + x2 = 0

Solving
0.5 + -4.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -4.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -4.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -4.5x + x2 = 0 + -0.5
-4.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-4.5x + x2 = -0.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = -0.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -0.5 + 5.0625

Combine like terms: -0.5 + 5.0625 = 4.5625
5.0625 + -4.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.136000936 and -2.136000936.


Subproblem 1
x + -2.25 = 2.136000936

Simplifying
x + -2.25 = 2.136000936

Reorder the terms:
-2.25 + x = 2.136000936

Solving
-2.25 + x = 2.136000936

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.136000936 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.136000936 + 2.25
x = 2.136000936 + 2.25

Combine like terms: 2.136000936 + 2.25 = 4.386000936
x = 4.386000936

Simplifying
x = 4.386000936


Subproblem 2
x + -2.25 = -2.136000936

Simplifying
x + -2.25 = -2.136000936

Reorder the terms:
-2.25 + x = -2.136000936

Solving
-2.25 + x = -2.136000936

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.136000936 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.136000936 + 2.25
x = -2.136000936 + 2.25

Combine like terms: -2.136000936 + 2.25 = 0.113999064
x = 0.113999064

Simplifying
x = 0.113999064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.386000936, 0.113999064}

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