-0.12x^2+0.72x+6.08=0

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Solution for -0.12x^2+0.72x+6.08=0 equation: 


Simplifying
-0.12x2 + 0.72x + 6.08 = 0

Reorder the terms:
6.08 + 0.72x + -0.12x2 = 0

Solving
6.08 + 0.72x + -0.12x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.12 the coefficient of the squared term: 

Divide each side by '-0.12'.
-50.66666667 + -6x + x2 = 0

Move the constant term to the right:

Add '50.66666667' to each side of the equation.
-50.66666667 + -6x + 50.66666667 + x2 = 0 + 50.66666667

Reorder the terms:
-50.66666667 + 50.66666667 + -6x + x2 = 0 + 50.66666667

Combine like terms: -50.66666667 + 50.66666667 = 0.00000000
0.00000000 + -6x + x2 = 0 + 50.66666667
-6x + x2 = 0 + 50.66666667

Combine like terms: 0 + 50.66666667 = 50.66666667
-6x + x2 = 50.66666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 50.66666667 + 9

Reorder the terms:
9 + -6x + x2 = 50.66666667 + 9

Combine like terms: 50.66666667 + 9 = 59.66666667
9 + -6x + x2 = 59.66666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 59.66666667

Calculate the square root of the right side: 7.724420151

Break this problem into two subproblems by setting 
(x + -3) equal to 7.724420151 and -7.724420151.


Subproblem 1
x + -3 = 7.724420151

Simplifying
x + -3 = 7.724420151

Reorder the terms:
-3 + x = 7.724420151

Solving
-3 + x = 7.724420151

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 7.724420151 + 3

Combine like terms: -3 + 3 = 0
0 + x = 7.724420151 + 3
x = 7.724420151 + 3

Combine like terms: 7.724420151 + 3 = 10.724420151
x = 10.724420151

Simplifying
x = 10.724420151


Subproblem 2
x + -3 = -7.724420151

Simplifying
x + -3 = -7.724420151

Reorder the terms:
-3 + x = -7.724420151

Solving
-3 + x = -7.724420151

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -7.724420151 + 3

Combine like terms: -3 + 3 = 0
0 + x = -7.724420151 + 3
x = -7.724420151 + 3

Combine like terms: -7.724420151 + 3 = -4.724420151
x = -4.724420151

Simplifying
x = -4.724420151


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.724420151, -4.724420151}

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