x^2-16.6x+9.6=0

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Solution for x^2-16.6x+9.6=0 equation: 


Simplifying
x2 + -16.6x + 9.6 = 0

Reorder the terms:
9.6 + -16.6x + x2 = 0

Solving
9.6 + -16.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9.6' to each side of the equation.
9.6 + -16.6x + -9.6 + x2 = 0 + -9.6

Reorder the terms:
9.6 + -9.6 + -16.6x + x2 = 0 + -9.6

Combine like terms: 9.6 + -9.6 = 0.0
0.0 + -16.6x + x2 = 0 + -9.6
-16.6x + x2 = 0 + -9.6

Combine like terms: 0 + -9.6 = -9.6
-16.6x + x2 = -9.6

The x term is -16.6x.  Take half its coefficient (-8.3).
Square it (68.89) and add it to both sides.

Add '68.89' to each side of the equation.
-16.6x + 68.89 + x2 = -9.6 + 68.89

Reorder the terms:
68.89 + -16.6x + x2 = -9.6 + 68.89

Combine like terms: -9.6 + 68.89 = 59.29
68.89 + -16.6x + x2 = 59.29

Factor a perfect square on the left side:
(x + -8.3)(x + -8.3) = 59.29

Calculate the square root of the right side: 7.7

Break this problem into two subproblems by setting 
(x + -8.3) equal to 7.7 and -7.7.


Subproblem 1
x + -8.3 = 7.7

Simplifying
x + -8.3 = 7.7

Reorder the terms:
-8.3 + x = 7.7

Solving
-8.3 + x = 7.7

Solving for variable 'x'.

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

Add '8.3' to each side of the equation.
-8.3 + 8.3 + x = 7.7 + 8.3

Combine like terms: -8.3 + 8.3 = 0.0
0.0 + x = 7.7 + 8.3
x = 7.7 + 8.3

Combine like terms: 7.7 + 8.3 = 16
x = 16

Simplifying
x = 16


Subproblem 2
x + -8.3 = -7.7

Simplifying
x + -8.3 = -7.7

Reorder the terms:
-8.3 + x = -7.7

Solving
-8.3 + x = -7.7

Solving for variable 'x'.

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

Add '8.3' to each side of the equation.
-8.3 + 8.3 + x = -7.7 + 8.3

Combine like terms: -8.3 + 8.3 = 0.0
0.0 + x = -7.7 + 8.3
x = -7.7 + 8.3

Combine like terms: -7.7 + 8.3 = 0.6
x = 0.6

Simplifying
x = 0.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16, 0.6}

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