-0.13x^2+2.3x-8=0

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Solution for -0.13x^2+2.3x-8=0 equation: 


Simplifying
-0.13x2 + 2.3x + -8 = 0

Reorder the terms:
-8 + 2.3x + -0.13x2 = 0

Solving
-8 + 2.3x + -0.13x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.13 the coefficient of the squared term: 

Divide each side by '-0.13'.
61.53846154 + -17.69230769x + x2 = 0

Move the constant term to the right:

Add '-61.53846154' to each side of the equation.
61.53846154 + -17.69230769x + -61.53846154 + x2 = 0 + -61.53846154

Reorder the terms:
61.53846154 + -61.53846154 + -17.69230769x + x2 = 0 + -61.53846154

Combine like terms: 61.53846154 + -61.53846154 = 0.00000000
0.00000000 + -17.69230769x + x2 = 0 + -61.53846154
-17.69230769x + x2 = 0 + -61.53846154

Combine like terms: 0 + -61.53846154 = -61.53846154
-17.69230769x + x2 = -61.53846154

The x term is -17.69230769x.  Take half its coefficient (-8.846153845).
Square it (78.25443785) and add it to both sides.

Add '78.25443785' to each side of the equation.
-17.69230769x + 78.25443785 + x2 = -61.53846154 + 78.25443785

Reorder the terms:
78.25443785 + -17.69230769x + x2 = -61.53846154 + 78.25443785

Combine like terms: -61.53846154 + 78.25443785 = 16.71597631
78.25443785 + -17.69230769x + x2 = 16.71597631

Factor a perfect square on the left side:
(x + -8.846153845)(x + -8.846153845) = 16.71597631

Calculate the square root of the right side: 4.088517618

Break this problem into two subproblems by setting 
(x + -8.846153845) equal to 4.088517618 and -4.088517618.


Subproblem 1
x + -8.846153845 = 4.088517618

Simplifying
x + -8.846153845 = 4.088517618

Reorder the terms:
-8.846153845 + x = 4.088517618

Solving
-8.846153845 + x = 4.088517618

Solving for variable 'x'.

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

Add '8.846153845' to each side of the equation.
-8.846153845 + 8.846153845 + x = 4.088517618 + 8.846153845

Combine like terms: -8.846153845 + 8.846153845 = 0.000000000
0.000000000 + x = 4.088517618 + 8.846153845
x = 4.088517618 + 8.846153845

Combine like terms: 4.088517618 + 8.846153845 = 12.934671463
x = 12.934671463

Simplifying
x = 12.934671463


Subproblem 2
x + -8.846153845 = -4.088517618

Simplifying
x + -8.846153845 = -4.088517618

Reorder the terms:
-8.846153845 + x = -4.088517618

Solving
-8.846153845 + x = -4.088517618

Solving for variable 'x'.

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

Add '8.846153845' to each side of the equation.
-8.846153845 + 8.846153845 + x = -4.088517618 + 8.846153845

Combine like terms: -8.846153845 + 8.846153845 = 0.000000000
0.000000000 + x = -4.088517618 + 8.846153845
x = -4.088517618 + 8.846153845

Combine like terms: -4.088517618 + 8.846153845 = 4.757636227
x = 4.757636227

Simplifying
x = 4.757636227


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.934671463, 4.757636227}

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