0=-2.595x^2+22.1x-9.85

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Solution for 0=-2.595x^2+22.1x-9.85 equation: 


Simplifying
0 = -2.595x2 + 22.1x + -9.85

Reorder the terms:
0 = -9.85 + 22.1x + -2.595x2

Solving
0 = -9.85 + 22.1x + -2.595x2

Solving for variable 'x'.

Combine like terms: 0 + 9.85 = 9.85
9.85 + -22.1x + 2.595x2 = -9.85 + 22.1x + -2.595x2 + 9.85 + -22.1x + 2.595x2

Reorder the terms:
9.85 + -22.1x + 2.595x2 = -9.85 + 9.85 + 22.1x + -22.1x + -2.595x2 + 2.595x2

Combine like terms: -9.85 + 9.85 = 0.00
9.85 + -22.1x + 2.595x2 = 0.00 + 22.1x + -22.1x + -2.595x2 + 2.595x2
9.85 + -22.1x + 2.595x2 = 22.1x + -22.1x + -2.595x2 + 2.595x2

Combine like terms: 22.1x + -22.1x = 0.0
9.85 + -22.1x + 2.595x2 = 0.0 + -2.595x2 + 2.595x2
9.85 + -22.1x + 2.595x2 = -2.595x2 + 2.595x2

Combine like terms: -2.595x2 + 2.595x2 = 0.000
9.85 + -22.1x + 2.595x2 = 0.000

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

Divide each side by '2.595'.
3.795761079 + -8.516377649x + x2 = 0

Move the constant term to the right:

Add '-3.795761079' to each side of the equation.
3.795761079 + -8.516377649x + -3.795761079 + x2 = 0 + -3.795761079

Reorder the terms:
3.795761079 + -3.795761079 + -8.516377649x + x2 = 0 + -3.795761079

Combine like terms: 3.795761079 + -3.795761079 = 0.000000000
0.000000000 + -8.516377649x + x2 = 0 + -3.795761079
-8.516377649x + x2 = 0 + -3.795761079

Combine like terms: 0 + -3.795761079 = -3.795761079
-8.516377649x + x2 = -3.795761079

The x term is -8.516377649x.  Take half its coefficient (-4.258188825).
Square it (18.13217207) and add it to both sides.

Add '18.13217207' to each side of the equation.
-8.516377649x + 18.13217207 + x2 = -3.795761079 + 18.13217207

Reorder the terms:
18.13217207 + -8.516377649x + x2 = -3.795761079 + 18.13217207

Combine like terms: -3.795761079 + 18.13217207 = 14.336410991
18.13217207 + -8.516377649x + x2 = 14.336410991

Factor a perfect square on the left side:
(x + -4.258188825)(x + -4.258188825) = 14.336410991

Calculate the square root of the right side: 3.786345334

Break this problem into two subproblems by setting 
(x + -4.258188825) equal to 3.786345334 and -3.786345334.


Subproblem 1
x + -4.258188825 = 3.786345334

Simplifying
x + -4.258188825 = 3.786345334

Reorder the terms:
-4.258188825 + x = 3.786345334

Solving
-4.258188825 + x = 3.786345334

Solving for variable 'x'.

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

Add '4.258188825' to each side of the equation.
-4.258188825 + 4.258188825 + x = 3.786345334 + 4.258188825

Combine like terms: -4.258188825 + 4.258188825 = 0.000000000
0.000000000 + x = 3.786345334 + 4.258188825
x = 3.786345334 + 4.258188825

Combine like terms: 3.786345334 + 4.258188825 = 8.044534159
x = 8.044534159

Simplifying
x = 8.044534159


Subproblem 2
x + -4.258188825 = -3.786345334

Simplifying
x + -4.258188825 = -3.786345334

Reorder the terms:
-4.258188825 + x = -3.786345334

Solving
-4.258188825 + x = -3.786345334

Solving for variable 'x'.

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

Add '4.258188825' to each side of the equation.
-4.258188825 + 4.258188825 + x = -3.786345334 + 4.258188825

Combine like terms: -4.258188825 + 4.258188825 = 0.000000000
0.000000000 + x = -3.786345334 + 4.258188825
x = -3.786345334 + 4.258188825

Combine like terms: -3.786345334 + 4.258188825 = 0.471843491
x = 0.471843491

Simplifying
x = 0.471843491


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.044534159, 0.471843491}

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