.18x^2-22x+223=0

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Solution for .18x^2-22x+223=0 equation:


Simplifying
0.18x2 + -22x + 223 = 0

Reorder the terms:
223 + -22x + 0.18x2 = 0

Solving
223 + -22x + 0.18x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.18'.
1238.888889 + -122.2222222x + x2 = 0

Move the constant term to the right:

Add '-1238.888889' to each side of the equation.
1238.888889 + -122.2222222x + -1238.888889 + x2 = 0 + -1238.888889

Reorder the terms:
1238.888889 + -1238.888889 + -122.2222222x + x2 = 0 + -1238.888889

Combine like terms: 1238.888889 + -1238.888889 = 0.000000
0.000000 + -122.2222222x + x2 = 0 + -1238.888889
-122.2222222x + x2 = 0 + -1238.888889

Combine like terms: 0 + -1238.888889 = -1238.888889
-122.2222222x + x2 = -1238.888889

The x term is -122.2222222x.  Take half its coefficient (-61.1111111).
Square it (3734.567900) and add it to both sides.

Add '3734.567900' to each side of the equation.
-122.2222222x + 3734.567900 + x2 = -1238.888889 + 3734.567900

Reorder the terms:
3734.567900 + -122.2222222x + x2 = -1238.888889 + 3734.567900

Combine like terms: -1238.888889 + 3734.567900 = 2495.679011
3734.567900 + -122.2222222x + x2 = 2495.679011

Factor a perfect square on the left side:
(x + -61.1111111)(x + -61.1111111) = 2495.679011

Calculate the square root of the right side: 49.956771423

Break this problem into two subproblems by setting 
(x + -61.1111111) equal to 49.956771423 and -49.956771423.

Subproblem 1

x + -61.1111111 = 49.956771423 Simplifying x + -61.1111111 = 49.956771423 Reorder the terms: -61.1111111 + x = 49.956771423 Solving -61.1111111 + x = 49.956771423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.1111111' to each side of the equation. -61.1111111 + 61.1111111 + x = 49.956771423 + 61.1111111 Combine like terms: -61.1111111 + 61.1111111 = 0.0000000 0.0000000 + x = 49.956771423 + 61.1111111 x = 49.956771423 + 61.1111111 Combine like terms: 49.956771423 + 61.1111111 = 111.067882523 x = 111.067882523 Simplifying x = 111.067882523

Subproblem 2

x + -61.1111111 = -49.956771423 Simplifying x + -61.1111111 = -49.956771423 Reorder the terms: -61.1111111 + x = -49.956771423 Solving -61.1111111 + x = -49.956771423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.1111111' to each side of the equation. -61.1111111 + 61.1111111 + x = -49.956771423 + 61.1111111 Combine like terms: -61.1111111 + 61.1111111 = 0.0000000 0.0000000 + x = -49.956771423 + 61.1111111 x = -49.956771423 + 61.1111111 Combine like terms: -49.956771423 + 61.1111111 = 11.154339677 x = 11.154339677 Simplifying x = 11.154339677

Solution

The solution to the problem is based on the solutions from the subproblems. x = {111.067882523, 11.154339677}

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