0.5x^2-3x+1.125=0

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Solution for 0.5x^2-3x+1.125=0 equation: 


Simplifying
0.5x2 + -3x + 1.125 = 0

Reorder the terms:
1.125 + -3x + 0.5x2 = 0

Solving
1.125 + -3x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
2.25 + -6x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -6x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -6x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -6x + x2 = 0 + -2.25
-6x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-6x + x2 = -2.25

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -2.25 + 9

Reorder the terms:
9 + -6x + x2 = -2.25 + 9

Combine like terms: -2.25 + 9 = 6.75
9 + -6x + x2 = 6.75

Factor a perfect square on the left side:
(x + -3)(x + -3) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(x + -3) equal to 2.598076211 and -2.598076211.


Subproblem 1
x + -3 = 2.598076211

Simplifying
x + -3 = 2.598076211

Reorder the terms:
-3 + x = 2.598076211

Solving
-3 + x = 2.598076211

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.598076211 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.598076211 + 3
x = 2.598076211 + 3

Combine like terms: 2.598076211 + 3 = 5.598076211
x = 5.598076211

Simplifying
x = 5.598076211


Subproblem 2
x + -3 = -2.598076211

Simplifying
x + -3 = -2.598076211

Reorder the terms:
-3 + x = -2.598076211

Solving
-3 + x = -2.598076211

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.598076211 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.598076211 + 3
x = -2.598076211 + 3

Combine like terms: -2.598076211 + 3 = 0.401923789
x = 0.401923789

Simplifying
x = 0.401923789


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.598076211, 0.401923789}

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