-0.3x^2+6.6x+14=0

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Solution for -0.3x^2+6.6x+14=0 equation: 


Simplifying
-0.3x2 + 6.6x + 14 = 0

Reorder the terms:
14 + 6.6x + -0.3x2 = 0

Solving
14 + 6.6x + -0.3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
-46.66666667 + -22x + x2 = 0

Move the constant term to the right:

Add '46.66666667' to each side of the equation.
-46.66666667 + -22x + 46.66666667 + x2 = 0 + 46.66666667

Reorder the terms:
-46.66666667 + 46.66666667 + -22x + x2 = 0 + 46.66666667

Combine like terms: -46.66666667 + 46.66666667 = 0.00000000
0.00000000 + -22x + x2 = 0 + 46.66666667
-22x + x2 = 0 + 46.66666667

Combine like terms: 0 + 46.66666667 = 46.66666667
-22x + x2 = 46.66666667

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 46.66666667 + 121

Reorder the terms:
121 + -22x + x2 = 46.66666667 + 121

Combine like terms: 46.66666667 + 121 = 167.66666667
121 + -22x + x2 = 167.66666667

Factor a perfect square on the left side:
(x + -11)(x + -11) = 167.66666667

Calculate the square root of the right side: 12.9486164

Break this problem into two subproblems by setting 
(x + -11) equal to 12.9486164 and -12.9486164.


Subproblem 1
x + -11 = 12.9486164

Simplifying
x + -11 = 12.9486164

Reorder the terms:
-11 + x = 12.9486164

Solving
-11 + x = 12.9486164

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 12.9486164 + 11

Combine like terms: -11 + 11 = 0
0 + x = 12.9486164 + 11
x = 12.9486164 + 11

Combine like terms: 12.9486164 + 11 = 23.9486164
x = 23.9486164

Simplifying
x = 23.9486164


Subproblem 2
x + -11 = -12.9486164

Simplifying
x + -11 = -12.9486164

Reorder the terms:
-11 + x = -12.9486164

Solving
-11 + x = -12.9486164

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -12.9486164 + 11

Combine like terms: -11 + 11 = 0
0 + x = -12.9486164 + 11
x = -12.9486164 + 11

Combine like terms: -12.9486164 + 11 = -1.9486164
x = -1.9486164

Simplifying
x = -1.9486164


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.9486164, -1.9486164}

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