8+5.6x-1.2x^2=0

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Solution for 8+5.6x-1.2x^2=0 equation: 


Simplifying
8 + 5.6x + -1.2x2 = 0

Solving
8 + 5.6x + -1.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.2 the coefficient of the squared term: 

Divide each side by '-1.2'.
-6.666666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -4.666666667x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -4.666666667x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 6.666666667
-4.666666667x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-4.666666667x + x2 = 6.666666667

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 6.666666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 6.666666667 + 5.444444448

Combine like terms: 6.666666667 + 5.444444448 = 12.111111115
5.444444448 + -4.666666667x + x2 = 12.111111115

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 12.111111115

Calculate the square root of the right side: 3.48010217

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 3.48010217 and -3.48010217.


Subproblem 1
x + -2.333333334 = 3.48010217

Simplifying
x + -2.333333334 = 3.48010217

Reorder the terms:
-2.333333334 + x = 3.48010217

Solving
-2.333333334 + x = 3.48010217

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 3.48010217 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 3.48010217 + 2.333333334
x = 3.48010217 + 2.333333334

Combine like terms: 3.48010217 + 2.333333334 = 5.813435504
x = 5.813435504

Simplifying
x = 5.813435504


Subproblem 2
x + -2.333333334 = -3.48010217

Simplifying
x + -2.333333334 = -3.48010217

Reorder the terms:
-2.333333334 + x = -3.48010217

Solving
-2.333333334 + x = -3.48010217

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -3.48010217 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -3.48010217 + 2.333333334
x = -3.48010217 + 2.333333334

Combine like terms: -3.48010217 + 2.333333334 = -1.146768836
x = -1.146768836

Simplifying
x = -1.146768836


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.813435504, -1.146768836}

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