0.6x^2+3.11x-9.6=0

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Solution for 0.6x^2+3.11x-9.6=0 equation: 


Simplifying
0.6x2 + 3.11x + -9.6 = 0

Reorder the terms:
-9.6 + 3.11x + 0.6x2 = 0

Solving
-9.6 + 3.11x + 0.6x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.6'.
-16 + 5.183333333x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 5.183333333x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 5.183333333x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 5.183333333x + x2 = 0 + 16
5.183333333x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
5.183333333x + x2 = 16

The x term is 5.183333333x.  Take half its coefficient (2.591666667).
Square it (6.716736113) and add it to both sides.

Add '6.716736113' to each side of the equation.
5.183333333x + 6.716736113 + x2 = 16 + 6.716736113

Reorder the terms:
6.716736113 + 5.183333333x + x2 = 16 + 6.716736113

Combine like terms: 16 + 6.716736113 = 22.716736113
6.716736113 + 5.183333333x + x2 = 22.716736113

Factor a perfect square on the left side:
(x + 2.591666667)(x + 2.591666667) = 22.716736113

Calculate the square root of the right side: 4.766207729

Break this problem into two subproblems by setting 
(x + 2.591666667) equal to 4.766207729 and -4.766207729.


Subproblem 1
x + 2.591666667 = 4.766207729

Simplifying
x + 2.591666667 = 4.766207729

Reorder the terms:
2.591666667 + x = 4.766207729

Solving
2.591666667 + x = 4.766207729

Solving for variable 'x'.

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

Add '-2.591666667' to each side of the equation.
2.591666667 + -2.591666667 + x = 4.766207729 + -2.591666667

Combine like terms: 2.591666667 + -2.591666667 = 0.000000000
0.000000000 + x = 4.766207729 + -2.591666667
x = 4.766207729 + -2.591666667

Combine like terms: 4.766207729 + -2.591666667 = 2.174541062
x = 2.174541062

Simplifying
x = 2.174541062


Subproblem 2
x + 2.591666667 = -4.766207729

Simplifying
x + 2.591666667 = -4.766207729

Reorder the terms:
2.591666667 + x = -4.766207729

Solving
2.591666667 + x = -4.766207729

Solving for variable 'x'.

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

Add '-2.591666667' to each side of the equation.
2.591666667 + -2.591666667 + x = -4.766207729 + -2.591666667

Combine like terms: 2.591666667 + -2.591666667 = 0.000000000
0.000000000 + x = -4.766207729 + -2.591666667
x = -4.766207729 + -2.591666667

Combine like terms: -4.766207729 + -2.591666667 = -7.357874396
x = -7.357874396

Simplifying
x = -7.357874396


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.174541062, -7.357874396}

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