.9x^2-6x-5=0

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Solution for .9x^2-6x-5=0 equation:


Simplifying
0.9x2 + -6x + -5 = 0

Reorder the terms:
-5 + -6x + 0.9x2 = 0

Solving
-5 + -6x + 0.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.9'.
-5.555555556 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '5.555555556' to each side of the equation.
-5.555555556 + -6.666666667x + 5.555555556 + x2 = 0 + 5.555555556

Reorder the terms:
-5.555555556 + 5.555555556 + -6.666666667x + x2 = 0 + 5.555555556

Combine like terms: -5.555555556 + 5.555555556 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + 5.555555556
-6.666666667x + x2 = 0 + 5.555555556

Combine like terms: 0 + 5.555555556 = 5.555555556
-6.666666667x + x2 = 5.555555556

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 5.555555556 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 5.555555556 + 11.11111112

Combine like terms: 5.555555556 + 11.11111112 = 16.666666676
11.11111112 + -6.666666667x + x2 = 16.666666676

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 16.666666676

Calculate the square root of the right side: 4.082482906

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 4.082482906 and -4.082482906.


Subproblem 1
x + -3.333333334 = 4.082482906

Simplifying
x + -3.333333334 = 4.082482906

Reorder the terms:
-3.333333334 + x = 4.082482906

Solving
-3.333333334 + x = 4.082482906

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 4.082482906 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 4.082482906 + 3.333333334
x = 4.082482906 + 3.333333334

Combine like terms: 4.082482906 + 3.333333334 = 7.41581624
x = 7.41581624

Simplifying
x = 7.41581624


Subproblem 2
x + -3.333333334 = -4.082482906

Simplifying
x + -3.333333334 = -4.082482906

Reorder the terms:
-3.333333334 + x = -4.082482906

Solving
-3.333333334 + x = -4.082482906

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -4.082482906 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -4.082482906 + 3.333333334
x = -4.082482906 + 3.333333334

Combine like terms: -4.082482906 + 3.333333334 = -0.749149572
x = -0.749149572

Simplifying
x = -0.749149572


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.41581624, -0.749149572}

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