0.9x^2-10x+22=0

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Solution for 0.9x^2-10x+22=0 equation: 


Simplifying
0.9x2 + -10x + 22 = 0

Reorder the terms:
22 + -10x + 0.9x2 = 0

Solving
22 + -10x + 0.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.9'.
24.44444444 + -11.11111111x + x2 = 0

Move the constant term to the right:

Add '-24.44444444' to each side of the equation.
24.44444444 + -11.11111111x + -24.44444444 + x2 = 0 + -24.44444444

Reorder the terms:
24.44444444 + -24.44444444 + -11.11111111x + x2 = 0 + -24.44444444

Combine like terms: 24.44444444 + -24.44444444 = 0.00000000
0.00000000 + -11.11111111x + x2 = 0 + -24.44444444
-11.11111111x + x2 = 0 + -24.44444444

Combine like terms: 0 + -24.44444444 = -24.44444444
-11.11111111x + x2 = -24.44444444

The x term is -11.11111111x.  Take half its coefficient (-5.555555555).
Square it (30.86419752) and add it to both sides.

Add '30.86419752' to each side of the equation.
-11.11111111x + 30.86419752 + x2 = -24.44444444 + 30.86419752

Reorder the terms:
30.86419752 + -11.11111111x + x2 = -24.44444444 + 30.86419752

Combine like terms: -24.44444444 + 30.86419752 = 6.41975308
30.86419752 + -11.11111111x + x2 = 6.41975308

Factor a perfect square on the left side:
(x + -5.555555555)(x + -5.555555555) = 6.41975308

Calculate the square root of the right side: 2.533723166

Break this problem into two subproblems by setting 
(x + -5.555555555) equal to 2.533723166 and -2.533723166.


Subproblem 1
x + -5.555555555 = 2.533723166

Simplifying
x + -5.555555555 = 2.533723166

Reorder the terms:
-5.555555555 + x = 2.533723166

Solving
-5.555555555 + x = 2.533723166

Solving for variable 'x'.

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

Add '5.555555555' to each side of the equation.
-5.555555555 + 5.555555555 + x = 2.533723166 + 5.555555555

Combine like terms: -5.555555555 + 5.555555555 = 0.000000000
0.000000000 + x = 2.533723166 + 5.555555555
x = 2.533723166 + 5.555555555

Combine like terms: 2.533723166 + 5.555555555 = 8.089278721
x = 8.089278721

Simplifying
x = 8.089278721


Subproblem 2
x + -5.555555555 = -2.533723166

Simplifying
x + -5.555555555 = -2.533723166

Reorder the terms:
-5.555555555 + x = -2.533723166

Solving
-5.555555555 + x = -2.533723166

Solving for variable 'x'.

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

Add '5.555555555' to each side of the equation.
-5.555555555 + 5.555555555 + x = -2.533723166 + 5.555555555

Combine like terms: -5.555555555 + 5.555555555 = 0.000000000
0.000000000 + x = -2.533723166 + 5.555555555
x = -2.533723166 + 5.555555555

Combine like terms: -2.533723166 + 5.555555555 = 3.021832389
x = 3.021832389

Simplifying
x = 3.021832389


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.089278721, 3.021832389}

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