3x^2-2.6x-0.95=0

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Solution for 3x^2-2.6x-0.95=0 equation: 


Simplifying
3x2 + -2.6x + -0.95 = 0

Reorder the terms:
-0.95 + -2.6x + 3x2 = 0

Solving
-0.95 + -2.6x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-0.3166666667 + -0.8666666667x + x2 = 0

Move the constant term to the right:

Add '0.3166666667' to each side of the equation.
-0.3166666667 + -0.8666666667x + 0.3166666667 + x2 = 0 + 0.3166666667

Reorder the terms:
-0.3166666667 + 0.3166666667 + -0.8666666667x + x2 = 0 + 0.3166666667

Combine like terms: -0.3166666667 + 0.3166666667 = 0.0000000000
0.0000000000 + -0.8666666667x + x2 = 0 + 0.3166666667
-0.8666666667x + x2 = 0 + 0.3166666667

Combine like terms: 0 + 0.3166666667 = 0.3166666667
-0.8666666667x + x2 = 0.3166666667

The x term is -0.8666666667x.  Take half its coefficient (-0.4333333334).
Square it (0.1877777778) and add it to both sides.

Add '0.1877777778' to each side of the equation.
-0.8666666667x + 0.1877777778 + x2 = 0.3166666667 + 0.1877777778

Reorder the terms:
0.1877777778 + -0.8666666667x + x2 = 0.3166666667 + 0.1877777778

Combine like terms: 0.3166666667 + 0.1877777778 = 0.5044444445
0.1877777778 + -0.8666666667x + x2 = 0.5044444445

Factor a perfect square on the left side:
(x + -0.4333333334)(x + -0.4333333334) = 0.5044444445

Calculate the square root of the right side: 0.710242525

Break this problem into two subproblems by setting 
(x + -0.4333333334) equal to 0.710242525 and -0.710242525.


Subproblem 1
x + -0.4333333334 = 0.710242525

Simplifying
x + -0.4333333334 = 0.710242525

Reorder the terms:
-0.4333333334 + x = 0.710242525

Solving
-0.4333333334 + x = 0.710242525

Solving for variable 'x'.

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

Add '0.4333333334' to each side of the equation.
-0.4333333334 + 0.4333333334 + x = 0.710242525 + 0.4333333334

Combine like terms: -0.4333333334 + 0.4333333334 = 0.0000000000
0.0000000000 + x = 0.710242525 + 0.4333333334
x = 0.710242525 + 0.4333333334

Combine like terms: 0.710242525 + 0.4333333334 = 1.1435758584
x = 1.1435758584

Simplifying
x = 1.1435758584


Subproblem 2
x + -0.4333333334 = -0.710242525

Simplifying
x + -0.4333333334 = -0.710242525

Reorder the terms:
-0.4333333334 + x = -0.710242525

Solving
-0.4333333334 + x = -0.710242525

Solving for variable 'x'.

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

Add '0.4333333334' to each side of the equation.
-0.4333333334 + 0.4333333334 + x = -0.710242525 + 0.4333333334

Combine like terms: -0.4333333334 + 0.4333333334 = 0.0000000000
0.0000000000 + x = -0.710242525 + 0.4333333334
x = -0.710242525 + 0.4333333334

Combine like terms: -0.710242525 + 0.4333333334 = -0.2769091916
x = -0.2769091916

Simplifying
x = -0.2769091916


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1435758584, -0.2769091916}

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