.75x^2-8.25x+18.5=0

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Solution for .75x^2-8.25x+18.5=0 equation: 


Simplifying
0.75x2 + -8.25x + 18.5 = 0

Reorder the terms:
18.5 + -8.25x + 0.75x2 = 0

Solving
18.5 + -8.25x + 0.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.75'.
24.66666667 + -11x + x2 = 0

Move the constant term to the right:

Add '-24.66666667' to each side of the equation.
24.66666667 + -11x + -24.66666667 + x2 = 0 + -24.66666667

Reorder the terms:
24.66666667 + -24.66666667 + -11x + x2 = 0 + -24.66666667

Combine like terms: 24.66666667 + -24.66666667 = 0.00000000
0.00000000 + -11x + x2 = 0 + -24.66666667
-11x + x2 = 0 + -24.66666667

Combine like terms: 0 + -24.66666667 = -24.66666667
-11x + x2 = -24.66666667

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -24.66666667 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -24.66666667 + 30.25

Combine like terms: -24.66666667 + 30.25 = 5.58333333
30.25 + -11x + x2 = 5.58333333

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 5.58333333

Calculate the square root of the right side: 2.362907812

Break this problem into two subproblems by setting 
(x + -5.5) equal to 2.362907812 and -2.362907812.


Subproblem 1
x + -5.5 = 2.362907812

Simplifying
x + -5.5 = 2.362907812

Reorder the terms:
-5.5 + x = 2.362907812

Solving
-5.5 + x = 2.362907812

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 2.362907812 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 2.362907812 + 5.5
x = 2.362907812 + 5.5

Combine like terms: 2.362907812 + 5.5 = 7.862907812
x = 7.862907812

Simplifying
x = 7.862907812


Subproblem 2
x + -5.5 = -2.362907812

Simplifying
x + -5.5 = -2.362907812

Reorder the terms:
-5.5 + x = -2.362907812

Solving
-5.5 + x = -2.362907812

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -2.362907812 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -2.362907812 + 5.5
x = -2.362907812 + 5.5

Combine like terms: -2.362907812 + 5.5 = 3.137092188
x = 3.137092188

Simplifying
x = 3.137092188


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.862907812, 3.137092188}

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